Abstract group 366912.a: $\GUnitary(2,13)$

• Label: 366912.a
• Order: \( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)
• Exponent: \( 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
• Nilpotent: no
• Solvable: no
• $\card{G^{\mathrm{ab}}}$: \( 2^{3} \cdot 3 \cdot 7 \)
• $\card{Z(G)}$: \( 2^{3} \cdot 3 \cdot 7 \)
• $\card{\Aut(G)}$: \( 2^{8} \cdot 3^{2} \cdot 7 \cdot 13 \)
• $\card{\mathrm{Out}(G)}$: \( 2^{5} \cdot 3 \)
• Perm deg.: $122$
• Trans deg.: $2352$
• Rank: $2$

Group information

Description:	$\GUnitary(2,13)$
Order:	\(366912\)\(\medspace = 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)
Exponent:	\(2184\)\(\medspace = 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
Automorphism group:	$C_2^4\times C_6\times \PSL(2,13).C_2$, of order \(209664\)\(\medspace = 2^{8} \cdot 3^{2} \cdot 7 \cdot 13 \)
Composition factors:	$C_2$ x 4, $C_3$, $C_7$, $\PSL(2,13)$
Derived length:	$1$

This group is nonabelian and nonsolvable.

Group statistics

Order	1	2	3	4	6	7	8	12	13	14	21	24	26	28	39	42	52	56	78	84	91	104	156	168	182	273	312	364	546	728	1092	2184
Elements	1	339	548	1068	2316	3282	1408	8688	168	11862	9840	11552	168	19512	336	33552	336	34656	336	78336	1008	672	672	121728	1008	2016	1344	2016	2016	4032	4032	8064	366912
Conjugacy classes	1	3	5	8	15	27	12	52	1	81	72	72	1	132	2	216	2	240	2	480	6	4	4	768	6	12	8	12	12	24	24	48	2352
Divisions	1	3	3	5	8	5	5	15	1	14	7	13	1	13	1	19	1	13	1	23	1	1	1	21	1	1	1	1	1	1	1	1	184
Autjugacy classes	1	3	3	4	7	7	5	14	1	15	9	17	1	16	1	19	1	17	1	26	1	1	1	29	1	1	1	1	1	1	1	1	208

Minimal presentations

Permutation degree:	$122$
Transitive degree:	$2352$
Rank:	$2$
Inequivalent generating pairs:	$190080$

Minimal degrees of faithful linear representations

	Over $\mathbb{C}$	Over $\mathbb{R}$	Over $\mathbb{Q}$
Irreducible	12	not computed	not computed
Arbitrary	not computed	not computed	not computed

Constructions

Groups of Lie type:	$\GUnitary(2,13)$
Permutation group:	Degree $122$ $\langle(1,2,8,24,56,79,89,103,84,111,107,108,77,106,112,95,53,22,49,62,33,12,3,5) \!\cdots\! \rangle$
Matrix group:	$\left\langle \left(\begin{array}{ll}\alpha^{68} & \alpha^{106} \\ \alpha^{164} & \alpha^{25} \\ \end{array}\right), \left(\begin{array}{ll}\alpha^{132} & 0 \\ 0 & \alpha^{132} \\ \end{array}\right), \left(\begin{array}{ll}\alpha^{121} & \alpha^{110} \\ 1 & \alpha^{110} \\ \end{array}\right), \left(\begin{array}{ll}\alpha^{150} & 0 \\ 0 & \alpha^{150} \\ \end{array}\right), \left(\begin{array}{ll}\alpha^{32} & 0 \\ 0 & \alpha^{32} \\ \end{array}\right), \left(\begin{array}{ll}\alpha^{120} & 0 \\ 0 & \alpha^{120} \\ \end{array}\right), \left(\begin{array}{ll}\alpha^{36} & \alpha^{158} \\ \alpha^{72} & \alpha^{12} \\ \end{array}\right), \left(\begin{array}{ll}\alpha^{159} & 0 \\ 0 & \alpha^{159} \\ \end{array}\right) \right\rangle \subseteq \GL_{2}(\F_{169}) = \GL_{2}(\F_{13}[\alpha]/(\alpha^{2} + 12 \alpha + 2))$
Direct product:	$C_3$ $\, \times\, $ $C_7$ $\, \times\, $ $(C_8.\PGL(2,13))$
Semidirect product:	not computed
Trans. wreath product:	not isomorphic to a non-trivial transitive wreath product
Non-split product:	$C_{168}$ . $(\PSL(2,13).C_2)$	$(C_{84}.\PSL(2,13))$ . $C_2^2$	$(C_{84}.\PSL(2,13).C_2)$ . $C_2$	$(C_{28}.\PSL(2,13).C_2)$ . $C_6$	all 24

Elements of the group are displayed as matrices in $\GUnitary(2,13)$.

Homology

Abelianization:	$C_{2} \times C_{84} \simeq C_{2} \times C_{4} \times C_{3} \times C_{7}$
Schur multiplier:	$C_{2}$
Commutator length:	$1$

Subgroups

There are 96356 subgroups in 960 conjugacy classes, 48 normal, and all normal subgroups are characteristic.

Characteristic subgroups are shown in this color.

Special subgroups

Center:	$Z \simeq$ $C_{168}$	$G/Z \simeq$ $\PSL(2,13).C_2$
Commutator:	$G' \simeq$ $C_2.\PSL(2,13)$	$G/G' \simeq$ $C_2\times C_{84}$
Frattini:	$\Phi \simeq$ $C_4$	$G/\Phi \simeq$ $C_{42}.\PSL(2,13).C_2$
Fitting:	$\operatorname{Fit} \simeq$ $C_{168}$	$G/\operatorname{Fit} \simeq$ $\PSL(2,13).C_2$
Radical:	$R \simeq$ $C_{168}$	$G/R \simeq$ $\PSL(2,13).C_2$
Socle:	$\operatorname{soc} \simeq$ $C_{42}$	$G/\operatorname{soc} \simeq$ $C_4\times \PSL(2,13).C_2$
2-Sylow subgroup:	$P_{ 2 } \simeq$ $D_8:C_4$
3-Sylow subgroup:	$P_{ 3 } \simeq$ $C_3^2$
7-Sylow subgroup:	$P_{ 7 } \simeq$ $C_7^2$
13-Sylow subgroup:	$P_{ 13 } \simeq$ $C_{13}$

Hi

Subgroup diagram and profile

Classes of subgroups up to conjugation

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Classes of subgroups up to automorphism

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Normal subgroups

Normal subgroups up to automorphism

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Classes of subgroups up to conjugation

Order 366912: $\GUnitary(2,13)$

Order 183456: $C_{168}.\PSL(2,13)$, $C_{84}.\PSL(2,13).C_2$, $C_{84}.\PSL(2,13).C_2$

Order 122304: $C_{56}.\PSL(2,13).C_2$

Order 91728: $C_{42}.\PSL(2,13).C_2$, $C_{42}.\PSL(2,13).C_2$, $C_{84}.\PSL(2,13)$

Order 61152: $C_{28}.\PSL(2,13).C_2$, $C_{56}.\PSL(2,13)$, $C_{28}.\PSL(2,13).C_2$

Order 52416: $C_{24}.\PSL(2,13).C_2$

Order 45864: $C_{42}.\PSL(2,13)$

Order 30576: $C_{14}.\PSL(2,13).C_2$, $C_{28}.\PSL(2,13)$, $C_{14}.\PSL(2,13).C_2$

Order 26208: $C_{24}.\PSL(2,13)$, $C_{12}.\PSL(2,13).C_2$, $C_{12}.\PSL(2,13).C_2$, $C_{91}.C_{12}^2.C_2$

Order 17472: $C_8.\PSL(2,13).C_2$

Order 15288: $C_{14}.\PSL(2,13)$

Order 13104: $C_{91}.C_{12}^2$, $C_{91}.(C_6\times C_{24})$, $C_6.\PSL(2,13).C_2$, $C_{91}.(C_6\times C_{24})$, $C_6.\PSL(2,13).C_2$, $C_{12}.\PSL(2,13)$

Order 8736: $C_{91}.C_6.C_4^2$ x 3, $C_{273}:(C_4\times C_8)$, $C_4.\PSL(2,13).C_2$, $C_8.\PSL(2,13)$, $C_4.\PSL(2,13).C_2$

Order 6552: $C_{13}:(C_3\times C_{168})$ x 2, $C_{13}:(C_6\times C_{84})$ x 2, $C_6.\PSL(2,13)$, $C_{13}:(C_6\times C_{84})$, $C_{13}:(C_3\times C_{168})$, $C_{728}:C_3^2$

Order 4704: $(C_7\times C_{84}).C_2^3$

Order 4368: $C_{13}:(C_2\times C_{168})$ x 3, $C_{13}:(C_4\times C_{84})$ x 3, $C_{13}:(C_2\times C_{168})$ x 3, $C_{273}:(C_2\times C_8)$, $C_{273}:C_4^2$, $C_{273}:(C_2\times C_8)$, $C_2.\PSL(2,13).C_2$, $C_4.\PSL(2,13)$, $C_2.\PSL(2,13).C_2$

Order 4032: $(C_6\times C_{84}).C_2^3$, $Q_8.(C_{84}\times S_3)$

Order 3744: $C_{13}.C_{12}^2.C_2$

Order 3276: $C_{13}:(C_3\times C_{84})$ x 4, $C_{13}:(C_3\times C_{84})$, $C_{13}:(C_6\times C_{42})$, $C_{364}:C_3^2$

Order 2912: $C_{91}:(C_4\times C_8)$

Order 2352: $C_7^2:(C_3\times \OD_{16})$ x 2, $C_7^2:(C_2\times C_{24})$ x 2, $C_7^2:(C_3\times \OD_{16})$, $C_7^2:(C_3\times D_4:C_2)$, $C_{14}\times C_{168}$

Order 2184: $C_{13}:C_{168}$ x 6, $C_{13}:(C_2\times C_{84})$ x 6, $C_{13}:(C_2\times C_{84})$ x 3, $C_{13}:C_{168}$ x 3, $C_{728}:C_3$ x 3, $C_{273}:(C_2\times C_4)$ x 2, $C_{273}:C_8$ x 2, $C_2.\PSL(2,13)$, $C_{273}:(C_2\times C_4)$, $C_{273}:C_8$, $C_{2184}$

Order 2016: $C_6.(C_{42}\times D_4)$, $\SL(2,3).C_{84}$, $Q_8.(C_3\times C_{84})$, $(C_{84}\times S_3).C_2^2$, $(C_3\times C_{84}).C_2^3$, $Q_8.(C_{42}\times S_3)$, $C_{84}.C_{12}.C_2$, $C_{84}.(C_2\times C_{12})$, $C_{84}.C_{12}.C_2$, $C_{12}\times C_{168}$

Order 1872: $C_{12}\times F_{13}$, $C_{156}.C_{12}$, $C_{312}:C_6$

Order 1638: $C_{39}:C_{42}$ x 2, $C_{39}:C_{42}$

Order 1568: $C_{56}.D_{14}$

Order 1456: $C_{364}:C_4$, $D_{13}:C_{56}$, $D_{13}\times C_{56}$

Order 1344: $\GL(2,3):C_{28}$, $D_8:C_{84}$, $D_{24}:C_{28}$

Order 1248: $C_8\times F_{13}$ x 3, $C_{104}:C_{12}$

Order 1176: $C_7\times C_{168}$ x 2, $C_7:C_{168}$ x 2, $D_{14}:C_{42}$ x 2, $D_7\times C_{84}$ x 2, $C_{14}\times C_{84}$, $C_{21}\times D_{28}$, $C_{28}.C_{42}$

Order 1092: $C_7\times F_{13}$ x 12, $C_{13}:C_{84}$ x 4, $C_{26}:C_{42}$ x 3, $C_{13}:C_{84}$ x 3, $C_{13}:C_{84}$ x 3, $C_{21}\times D_{26}$, $C_{1092}$, $C_{13}:C_{84}$

Order 1008: $D_{12}:C_{42}$ x 2, $C_6\times C_{168}$ x 2, $C_{12}.C_{84}$ x 2, $C_{24}:C_{42}$ x 2, $C_{24}:C_{42}$ x 2, $S_3\times C_{168}$ x 2, $\SL(2,3):C_{42}$, $C_{21}\times \GL(2,3)$, $C_{42}.S_4$, $C_{12}\times C_{84}$, $C_{24}.C_{42}$, $C_{21}\times D_{24}$

Order 936: $C_{39}:C_{24}$ x 2, $C_6\times F_{13}$ x 2, $C_{156}:C_6$, $C_{312}:C_3$, $C_{39}:C_{24}$

Order 819: $C_{273}:C_3$

Order 784: $C_{56}:C_{14}$ x 2, $D_7\times C_{56}$ x 2, $C_{14}\times C_{56}$, $C_{28}.C_{28}$, $D_{28}:C_{14}$

Order 728: $C_{13}:C_{56}$ x 2, $C_{26}:C_{28}$ x 2, $C_{728}$, $C_{13}:C_{56}$, $D_{13}\times C_{28}$

Order 672: $C_4\times C_{168}$ x 3, $D_{12}.C_{28}$ x 2, $C_{56}.A_4$ x 2, $D_4:C_{84}$ x 2, $D_{12}:C_{28}$ x 2, $\OD_{16}:C_{42}$ x 2, $D_{24}:C_{14}$, $C_{24}.D_{14}$, $\SL(2,3):C_{28}$, $C_8.C_{84}$, $C_{24}.C_{28}$, $\GL(2,3):C_{14}$, $D_8:C_{42}$

Order 624: $C_{104}:C_6$ x 3, $C_4\times F_{13}$ x 3, $D_{13}:C_{24}$ x 3, $C_{24}\times D_{13}$, $C_{156}:C_4$, $D_{13}:C_{24}$

Order 588: $C_{21}\times D_{14}$ x 2, $C_7\times C_{84}$ x 2, $C_7:C_{84}$ x 2, $C_{14}\times C_{42}$

Order 576: $\GL(2,3):C_{12}$, $D_{24}:C_{12}$

Order 546: $C_{13}:C_{42}$ x 6, $C_{13}:C_{42}$ x 3, $C_{21}\times D_{13}$ x 2, $C_{546}$

Order 504: $C_3\times C_{168}$ x 4, $C_3:C_{168}$ x 2, $C_6\times C_{84}$ x 2, $D_6:C_{42}$ x 2, $C_{21}\times D_{12}$ x 2, $S_3\times C_{84}$ x 2, $C_{12}.C_{42}$ x 2, $C_{21}\times \SL(2,3)$

Order 468: $C_3\times F_{13}$ x 4, $C_{78}:C_6$, $C_{156}:C_3$, $C_{39}:C_{12}$

Order 448: $D_8:C_{28}$

Order 416: $C_{104}:C_4$

Order 392: $C_{14}\wr C_2$ x 2, $D_7\times C_{28}$ x 2, $C_7\times C_{56}$ x 2, $C_7:C_{56}$ x 2, $C_{14}\times C_{28}$, $C_7\times D_{28}$, $C_7^2:Q_8$

Order 364: $C_{13}:C_{28}$ x 4, $C_7\times D_{26}$, $C_{364}$, $C_{13}:C_{28}$

Order 336: $C_2\times C_{168}$ x 11, $\OD_{16}\times C_{21}$ x 3, $C_4\times C_{84}$ x 3, $C_{12}.C_{28}$ x 2, $C_{168}:C_2$ x 2, $C_{168}:C_2$ x 2, $S_3\times C_{56}$ x 2, $C_{168}:C_2$ x 2, $D_7\times C_{24}$ x 2, $D_4:C_{42}$ x 2, $D_{12}:C_{14}$ x 2, $\SL(2,3):C_{14}$ x 2, $\SD_{16}\times C_{21}$ x 2, $C_{21}:Q_{16}$, $C_7\times D_{24}$, $C_{21}:\OD_{16}$, $D_{28}:C_6$, $C_7\times \GL(2,3)$, $C_{14}.S_4$, $Q_{16}\times C_{21}$, $D_8\times C_{21}$

Order 312: $C_{13}:C_{24}$ x 6, $C_2\times F_{13}$ x 6, $C_{52}:C_6$ x 3, $C_{13}:C_{24}$ x 3, $C_{13}:C_{24}$ x 3, $C_{26}:C_{12}$ x 2, $C_{13}:C_{24}$ x 2, $C_{312}$, $C_{13}:C_{24}$, $C_{12}\times D_{13}$

Order 294: $C_7\times C_{42}$ x 2, $D_7\times C_{21}$ x 2

Order 288: $C_{24}.D_6$ x 2, $C_{12}\wr C_2$ x 2, $\GL(2,3):C_6$, $D_{24}:C_6$, $C_{24}.A_4$, $\SL(2,3):C_{12}$, $C_{12}\times C_{24}$, $C_{24}.C_{12}$

Order 273: $C_{13}:C_{21}$ x 3, $C_{273}$

Order 252: $C_3\times C_{84}$ x 4, $S_3\times C_{42}$ x 2, $C_3:C_{84}$ x 2, $C_6\times C_{42}$

Order 234: $C_{39}:C_6$ x 2, $C_{39}:C_6$

Order 224: $D_4:C_{28}$ x 2, $\OD_{16}:C_{14}$ x 2, $C_8.D_{14}$, $C_8.C_{28}$, $C_4\times C_{56}$, $D_8:C_{14}$

Order 208: $C_8\times D_{13}$, $C_{52}:C_4$, $D_{13}:C_8$

Order 196: $C_7\times C_{28}$ x 2, $C_7:C_{28}$ x 2, $C_7\times D_{14}$ x 2, $C_{14}^2$

Order 192: $\GL(2,3):C_4$, $D_8:C_{12}$, $D_{24}:C_4$

Order 182: $C_7\times D_{13}$ x 2, $C_{182}$

Order 168: $C_{168}$ x 21, $C_2\times C_{84}$ x 12, $D_4\times C_{21}$ x 3, $Q_8\times C_{21}$ x 2, $C_7:C_{24}$ x 2, $D_6:C_{14}$ x 2, $C_7\times D_{12}$ x 2, $S_3\times C_{28}$ x 2, $C_3:C_{56}$ x 2, $C_{21}:Q_8$ x 2, $C_{21}:D_4$ x 2, $C_{12}\times D_7$ x 2, $C_7\times \SL(2,3)$ x 2, $C_3\times D_{28}$, $C_{21}:Q_8$

Order 156: $F_{13}$ x 12, $C_{13}:C_{12}$ x 4, $C_{26}:C_6$ x 3, $C_{13}:C_{12}$ x 3, $C_{13}:C_{12}$ x 3, $C_{156}$, $C_{13}:C_{12}$, $C_3\times D_{26}$

Order 147: $C_7\times C_{21}$

Order 144: $C_{12}.C_{12}$ x 2, $C_{24}:C_6$ x 2, $C_{24}:C_6$ x 2, $S_3\times C_{24}$ x 2, $D_{12}:C_6$ x 2, $C_6\times C_{24}$ x 2, $C_3^2:Q_{16}$, $C_3\times D_{24}$, $\SL(2,3):C_6$, $C_3\times \GL(2,3)$, $C_6.S_4$, $C_{12}^2$

Order 126: $C_3\times C_{42}$ x 2, $S_3\times C_{21}$ x 2

Order 117: $C_{39}:C_3$

Order 112: $C_2\times C_{56}$ x 7, $C_7\times \OD_{16}$ x 3, $D_4:C_{14}$ x 2, $C_{56}:C_2$ x 2, $C_8\times D_7$ x 2, $C_7\times \SD_{16}$ x 2, $C_7:\OD_{16}$, $D_{28}:C_2$, $C_7\times Q_{16}$, $C_7\times D_8$, $C_4\times C_{28}$

Order 104: $C_{13}:C_8$ x 2, $C_{26}:C_4$ x 2, $C_4\times D_{13}$, $C_{104}$, $C_{13}:C_8$

Order 98: $C_7\times C_{14}$ x 2, $C_7\times D_7$ x 2

Order 96: $C_4\times C_{24}$ x 3, $C_8.A_4$ x 2, $D_4:C_{12}$ x 2, $\OD_{16}:C_6$ x 2, $D_{12}:C_4$ x 2, $C_8.D_6$ x 2, $\Unitary(2,3)$, $C_8.C_{12}$, $C_{24}.C_4$, $\GL(2,3):C_2$, $D_8:C_6$, $D_{24}:C_2$

Order 91: $C_{91}$

Order 84: $C_{84}$ x 23, $C_2\times C_{42}$ x 8, $C_7:C_{12}$ x 2, $C_3:C_{28}$ x 2, $S_3\times C_{14}$ x 2, $C_3\times D_{14}$ x 2

Order 78: $C_{13}:C_6$ x 6, $C_{13}:C_6$ x 3, $C_3\times D_{13}$ x 2, $C_{78}$

Order 72: $C_3\times C_{24}$ x 4, $C_6\times C_{12}$ x 2, $C_6\wr C_2$ x 2, $C_3\times D_{12}$ x 2, $S_3\times C_{12}$ x 2, $C_3^2:Q_8$ x 2, $C_3:C_{24}$ x 2, $C_3\times \SL(2,3)$

Order 64: $D_8:C_4$

Order 63: $C_3\times C_{21}$

Order 56: $C_{56}$ x 13, $C_2\times C_{28}$ x 7, $C_7\times D_4$ x 3, $C_7:D_4$ x 2, $C_4\times D_7$ x 2, $C_7\times Q_8$ x 2, $C_7:C_8$ x 2, $D_{28}$, $C_7:Q_8$

Order 52: $C_{13}:C_4$ x 4, $D_{26}$, $C_{52}$, $C_{13}:C_4$

Order 49: $C_7^2$

Order 48: $C_2\times C_{24}$ x 7, $C_3\times \OD_{16}$ x 3, $C_4\times C_{12}$ x 3, $C_{24}:C_2$ x 2, $C_{24}:C_2$ x 2, $D_4:C_6$ x 2, $S_3\times C_8$ x 2, $D_{12}:C_2$ x 2, $\SL(2,3):C_2$ x 2, $C_3\times \SD_{16}$ x 2, $C_3:\OD_{16}$ x 2, $C_3:Q_{16}$, $D_{24}$, $\GL(2,3)$, $C_2.S_4$, $C_3\times Q_{16}$, $C_3\times D_8$

Order 42: $C_{42}$ x 19, $C_3\times D_7$ x 2, $S_3\times C_7$ x 2

Order 39: $C_{13}:C_3$ x 3, $C_{39}$

Order 36: $C_3\times C_{12}$ x 4, $C_3:C_{12}$ x 2, $C_6\times S_3$ x 2, $C_6^2$

Order 32: $\OD_{16}:C_2$ x 2, $C_4\wr C_2$ x 2, $D_8:C_2$, $C_4\times C_8$, $C_8.C_4$

Order 28: $C_{28}$ x 13, $C_2\times C_{14}$ x 6, $D_{14}$ x 2, $C_7:C_4$ x 2

Order 26: $D_{13}$ x 2, $C_{26}$

Order 24: $C_{24}$ x 13, $C_2\times C_{12}$ x 8, $C_3\times D_4$ x 3, $C_3:D_4$ x 2, $D_{12}$ x 2, $C_4\times S_3$ x 2, $C_3:Q_8$ x 2, $\SL(2,3)$ x 2, $C_3\times Q_8$ x 2, $C_3:C_8$ x 2

Order 21: $C_{21}$ x 7

Order 18: $C_3\times C_6$ x 2, $C_3\times S_3$ x 2

Order 16: $\OD_{16}$ x 3, $C_2\times C_8$ x 3, $\SD_{16}$ x 2, $D_4:C_2$ x 2, $Q_{16}$, $D_8$, $C_4^2$

Order 14: $C_{14}$ x 14, $D_7$ x 2

Order 13: $C_{13}$

Order 12: $C_{12}$ x 15, $C_2\times C_6$ x 4, $D_6$ x 2, $C_3:C_4$ x 2

Order 9: $C_3^2$

Order 8: $C_8$ x 5, $D_4$ x 3, $C_2\times C_4$ x 3, $Q_8$ x 2

Order 7: $C_7$ x 5

Order 6: $C_6$ x 8, $S_3$ x 2

Order 4: $C_4$ x 5, $C_2^2$ x 2

Order 3: $C_3$ x 3

Order 2: $C_2$ x 3

Order 1: $C_1$

Classes of subgroups up to automorphism

Order 366912: $\GUnitary(2,13)$

Order 183456: $C_{168}.\PSL(2,13)$, $C_{84}.\PSL(2,13).C_2$, $C_{84}.\PSL(2,13).C_2$

Order 122304: $C_{56}.\PSL(2,13).C_2$

Order 91728: $C_{42}.\PSL(2,13).C_2$, $C_{42}.\PSL(2,13).C_2$, $C_{84}.\PSL(2,13)$

Order 61152: $C_{28}.\PSL(2,13).C_2$, $C_{56}.\PSL(2,13)$, $C_{28}.\PSL(2,13).C_2$

Order 52416: $C_{24}.\PSL(2,13).C_2$

Order 45864: $C_{42}.\PSL(2,13)$

Order 30576: $C_{14}.\PSL(2,13).C_2$, $C_{28}.\PSL(2,13)$, $C_{14}.\PSL(2,13).C_2$

Order 26208: $C_{24}.\PSL(2,13)$, $C_{12}.\PSL(2,13).C_2$, $C_{12}.\PSL(2,13).C_2$, $C_{91}.C_{12}^2.C_2$

Order 17472: $C_8.\PSL(2,13).C_2$

Order 15288: $C_{14}.\PSL(2,13)$

Order 13104: $C_{91}.C_{12}^2$, $C_{91}.(C_6\times C_{24})$, $C_6.\PSL(2,13).C_2$, $C_{91}.(C_6\times C_{24})$, $C_6.\PSL(2,13).C_2$, $C_{12}.\PSL(2,13)$

Order 8736: $C_{91}.C_6.C_4^2$ x 2, $C_{273}:(C_4\times C_8)$, $C_4.\PSL(2,13).C_2$, $C_8.\PSL(2,13)$, $C_4.\PSL(2,13).C_2$

Order 6552: $C_{13}:(C_3\times C_{168})$ x 2, $C_6.\PSL(2,13)$, $C_{13}:(C_6\times C_{84})$, $C_{13}:(C_6\times C_{84})$, $C_{13}:(C_3\times C_{168})$, $C_{728}:C_3^2$

Order 4704: $(C_7\times C_{84}).C_2^3$

Order 4368: $C_{13}:(C_2\times C_{168})$ x 2, $C_{13}:(C_4\times C_{84})$ x 2, $C_{13}:(C_2\times C_{168})$ x 2, $C_{273}:(C_2\times C_8)$, $C_{273}:C_4^2$, $C_{273}:(C_2\times C_8)$, $C_2.\PSL(2,13).C_2$, $C_4.\PSL(2,13)$, $C_2.\PSL(2,13).C_2$

Order 4032: $(C_6\times C_{84}).C_2^3$, $Q_8.(C_{84}\times S_3)$

Order 3744: $C_{13}.C_{12}^2.C_2$

Order 3276: $C_{13}:(C_3\times C_{84})$, $C_{13}:(C_3\times C_{84})$, $C_{13}:(C_6\times C_{42})$, $C_{364}:C_3^2$

Order 2912: $C_{91}:(C_4\times C_8)$

Order 2352: $C_7^2:(C_3\times \OD_{16})$ x 2, $C_7^2:(C_2\times C_{24})$ x 2, $C_7^2:(C_3\times \OD_{16})$, $C_7^2:(C_3\times D_4:C_2)$, $C_{14}\times C_{168}$

Order 2184: $C_{13}:C_{168}$ x 4, $C_{13}:(C_2\times C_{84})$ x 2, $C_{13}:C_{168}$ x 2, $C_{13}:(C_2\times C_{84})$ x 2, $C_{273}:C_8$ x 2, $C_{728}:C_3$ x 2, $C_{273}:(C_2\times C_4)$, $C_2.\PSL(2,13)$, $C_{273}:(C_2\times C_4)$, $C_{273}:C_8$, $C_{2184}$

Order 2016: $C_6.(C_{42}\times D_4)$, $\SL(2,3).C_{84}$, $Q_8.(C_3\times C_{84})$, $(C_{84}\times S_3).C_2^2$, $(C_3\times C_{84}).C_2^3$, $Q_8.(C_{42}\times S_3)$, $C_{84}.C_{12}.C_2$, $C_{84}.(C_2\times C_{12})$, $C_{84}.C_{12}.C_2$, $C_{12}\times C_{168}$

Order 1872: $C_{12}\times F_{13}$, $C_{156}.C_{12}$, $C_{312}:C_6$

Order 1638: $C_{39}:C_{42}$, $C_{39}:C_{42}$

Order 1568: $C_{56}.D_{14}$

Order 1456: $C_{364}:C_4$, $D_{13}:C_{56}$, $D_{13}\times C_{56}$

Order 1344: $\GL(2,3):C_{28}$, $D_8:C_{84}$, $D_{24}:C_{28}$

Order 1248: $C_8\times F_{13}$ x 2, $C_{104}:C_{12}$

Order 1176: $C_7\times C_{168}$ x 2, $C_7:C_{168}$ x 2, $D_{14}:C_{42}$ x 2, $D_7\times C_{84}$ x 2, $C_{14}\times C_{84}$, $C_{21}\times D_{28}$, $C_{28}.C_{42}$

Order 1092: $C_{26}:C_{42}$ x 2, $C_7\times F_{13}$ x 2, $C_{13}:C_{84}$ x 2, $C_{13}:C_{84}$ x 2, $C_{21}\times D_{26}$, $C_{13}:C_{84}$, $C_{1092}$, $C_{13}:C_{84}$

Order 1008: $D_{12}:C_{42}$ x 2, $C_6\times C_{168}$ x 2, $C_{12}.C_{84}$ x 2, $C_{24}:C_{42}$ x 2, $C_{24}:C_{42}$ x 2, $S_3\times C_{168}$ x 2, $\SL(2,3):C_{42}$, $C_{21}\times \GL(2,3)$, $C_{42}.S_4$, $C_{12}\times C_{84}$, $C_{24}.C_{42}$, $C_{21}\times D_{24}$

Order 936: $C_{39}:C_{24}$ x 2, $C_{156}:C_6$, $C_{312}:C_3$, $C_{39}:C_{24}$, $C_6\times F_{13}$

Order 819: $C_{273}:C_3$

Order 784: $C_{56}:C_{14}$ x 2, $D_7\times C_{56}$ x 2, $C_{14}\times C_{56}$, $C_{28}.C_{28}$, $D_{28}:C_{14}$

Order 728: $C_{13}:C_{56}$ x 2, $C_{728}$, $C_{26}:C_{28}$, $C_{13}:C_{56}$, $D_{13}\times C_{28}$

Order 672: $C_4\times C_{168}$ x 3, $D_{12}.C_{28}$ x 2, $C_{56}.A_4$ x 2, $D_4:C_{84}$ x 2, $D_{12}:C_{28}$ x 2, $\OD_{16}:C_{42}$ x 2, $D_{24}:C_{14}$, $C_{24}.D_{14}$, $\SL(2,3):C_{28}$, $C_8.C_{84}$, $C_{24}.C_{28}$, $\GL(2,3):C_{14}$, $D_8:C_{42}$

Order 624: $C_{104}:C_6$ x 2, $C_4\times F_{13}$ x 2, $D_{13}:C_{24}$ x 2, $C_{24}\times D_{13}$, $C_{156}:C_4$, $D_{13}:C_{24}$

Order 588: $C_{21}\times D_{14}$ x 2, $C_7\times C_{84}$ x 2, $C_7:C_{84}$ x 2, $C_{14}\times C_{42}$

Order 576: $\GL(2,3):C_{12}$, $D_{24}:C_{12}$

Order 546: $C_{13}:C_{42}$ x 2, $C_{13}:C_{42}$ x 2, $C_{546}$, $C_{21}\times D_{13}$

Order 504: $C_3\times C_{168}$ x 4, $C_3:C_{168}$ x 2, $C_6\times C_{84}$ x 2, $D_6:C_{42}$ x 2, $C_{21}\times D_{12}$ x 2, $S_3\times C_{84}$ x 2, $C_{12}.C_{42}$ x 2, $C_{21}\times \SL(2,3)$

Order 468: $C_{78}:C_6$, $C_3\times F_{13}$, $C_{156}:C_3$, $C_{39}:C_{12}$

Order 448: $D_8:C_{28}$

Order 416: $C_{104}:C_4$

Order 392: $C_{14}\wr C_2$ x 2, $D_7\times C_{28}$ x 2, $C_7\times C_{56}$ x 2, $C_7:C_{56}$ x 2, $C_{14}\times C_{28}$, $C_7\times D_{28}$, $C_7^2:Q_8$

Order 364: $C_7\times D_{26}$, $C_{13}:C_{28}$, $C_{364}$, $C_{13}:C_{28}$

Order 336: $C_2\times C_{168}$ x 9, $\OD_{16}\times C_{21}$ x 3, $C_4\times C_{84}$ x 3, $C_{12}.C_{28}$ x 2, $C_{168}:C_2$ x 2, $C_{168}:C_2$ x 2, $S_3\times C_{56}$ x 2, $C_{168}:C_2$ x 2, $D_7\times C_{24}$ x 2, $D_4:C_{42}$ x 2, $D_{12}:C_{14}$ x 2, $\SL(2,3):C_{14}$ x 2, $\SD_{16}\times C_{21}$ x 2, $C_{21}:Q_{16}$, $C_7\times D_{24}$, $C_{21}:\OD_{16}$, $D_{28}:C_6$, $C_7\times \GL(2,3)$, $C_{14}.S_4$, $Q_{16}\times C_{21}$, $D_8\times C_{21}$

Order 312: $C_{13}:C_{24}$ x 4, $C_{52}:C_6$ x 2, $C_2\times F_{13}$ x 2, $C_{13}:C_{24}$ x 2, $C_{13}:C_{24}$ x 2, $C_{13}:C_{24}$ x 2, $C_{312}$, $C_{26}:C_{12}$, $C_{13}:C_{24}$, $C_{12}\times D_{13}$

Order 294: $C_7\times C_{42}$ x 2, $D_7\times C_{21}$ x 2

Order 288: $C_{24}.D_6$ x 2, $C_{12}\wr C_2$ x 2, $\GL(2,3):C_6$, $D_{24}:C_6$, $C_{24}.A_4$, $\SL(2,3):C_{12}$, $C_{12}\times C_{24}$, $C_{24}.C_{12}$

Order 273: $C_{13}:C_{21}$ x 2, $C_{273}$

Order 252: $C_3\times C_{84}$ x 3, $S_3\times C_{42}$ x 2, $C_3:C_{84}$ x 2, $C_6\times C_{42}$

Order 234: $C_{39}:C_6$, $C_{39}:C_6$

Order 224: $D_4:C_{28}$ x 2, $\OD_{16}:C_{14}$ x 2, $C_8.D_{14}$, $C_8.C_{28}$, $C_4\times C_{56}$, $D_8:C_{14}$

Order 208: $C_8\times D_{13}$, $C_{52}:C_4$, $D_{13}:C_8$

Order 196: $C_7\times C_{28}$ x 2, $C_7:C_{28}$ x 2, $C_7\times D_{14}$ x 2, $C_{14}^2$

Order 192: $\GL(2,3):C_4$, $D_8:C_{12}$, $D_{24}:C_4$

Order 182: $C_{182}$, $C_7\times D_{13}$

Order 168: $C_{168}$ x 17, $C_2\times C_{84}$ x 9, $D_4\times C_{21}$ x 3, $Q_8\times C_{21}$ x 2, $C_7:C_{24}$ x 2, $D_6:C_{14}$ x 2, $C_7\times D_{12}$ x 2, $S_3\times C_{28}$ x 2, $C_3:C_{56}$ x 2, $C_{21}:Q_8$ x 2, $C_{21}:D_4$ x 2, $C_{12}\times D_7$ x 2, $C_7\times \SL(2,3)$ x 2, $C_3\times D_{28}$, $C_{21}:Q_8$

Order 156: $C_{26}:C_6$ x 2, $F_{13}$ x 2, $C_{13}:C_{12}$ x 2, $C_{13}:C_{12}$ x 2, $C_{13}:C_{12}$, $C_{156}$, $C_{13}:C_{12}$, $C_3\times D_{26}$

Order 147: $C_7\times C_{21}$

Order 144: $C_{12}.C_{12}$ x 2, $C_{24}:C_6$ x 2, $C_{24}:C_6$ x 2, $S_3\times C_{24}$ x 2, $D_{12}:C_6$ x 2, $C_6\times C_{24}$ x 2, $C_3^2:Q_{16}$, $C_3\times D_{24}$, $\SL(2,3):C_6$, $C_3\times \GL(2,3)$, $C_6.S_4$, $C_{12}^2$

Order 126: $C_3\times C_{42}$ x 2, $S_3\times C_{21}$ x 2

Order 117: $C_{39}:C_3$

Order 112: $C_2\times C_{56}$ x 5, $C_7\times \OD_{16}$ x 3, $D_4:C_{14}$ x 2, $C_{56}:C_2$ x 2, $C_8\times D_7$ x 2, $C_7\times \SD_{16}$ x 2, $C_7:\OD_{16}$, $D_{28}:C_2$, $C_7\times Q_{16}$, $C_7\times D_8$, $C_4\times C_{28}$

Order 104: $C_{13}:C_8$ x 2, $C_4\times D_{13}$, $C_{104}$, $C_{26}:C_4$, $C_{13}:C_8$

Order 98: $C_7\times C_{14}$ x 2, $C_7\times D_7$ x 2

Order 96: $C_4\times C_{24}$ x 3, $C_8.A_4$ x 2, $D_4:C_{12}$ x 2, $\OD_{16}:C_6$ x 2, $D_{12}:C_4$ x 2, $C_8.D_6$ x 2, $\Unitary(2,3)$, $C_8.C_{12}$, $C_{24}.C_4$, $\GL(2,3):C_2$, $D_8:C_6$, $D_{24}:C_2$

Order 91: $C_{91}$

Order 84: $C_{84}$ x 14, $C_2\times C_{42}$ x 6, $C_7:C_{12}$ x 2, $C_3:C_{28}$ x 2, $S_3\times C_{14}$ x 2, $C_3\times D_{14}$ x 2

Order 78: $C_{13}:C_6$ x 2, $C_{13}:C_6$ x 2, $C_{78}$, $C_3\times D_{13}$

Order 72: $C_3\times C_{24}$ x 4, $C_6\times C_{12}$ x 2, $C_6\wr C_2$ x 2, $C_3\times D_{12}$ x 2, $S_3\times C_{12}$ x 2, $C_3^2:Q_8$ x 2, $C_3:C_{24}$ x 2, $C_3\times \SL(2,3)$

Order 64: $D_8:C_4$

Order 63: $C_3\times C_{21}$

Order 56: $C_{56}$ x 9, $C_2\times C_{28}$ x 5, $C_7\times D_4$ x 3, $C_7:D_4$ x 2, $C_4\times D_7$ x 2, $C_7\times Q_8$ x 2, $C_7:C_8$ x 2, $D_{28}$, $C_7:Q_8$

Order 52: $D_{26}$, $C_{13}:C_4$, $C_{52}$, $C_{13}:C_4$

Order 49: $C_7^2$

Order 48: $C_2\times C_{24}$ x 7, $C_3\times \OD_{16}$ x 3, $C_4\times C_{12}$ x 3, $C_{24}:C_2$ x 2, $C_{24}:C_2$ x 2, $D_4:C_6$ x 2, $S_3\times C_8$ x 2, $D_{12}:C_2$ x 2, $\SL(2,3):C_2$ x 2, $C_3\times \SD_{16}$ x 2, $C_3:\OD_{16}$ x 2, $C_3:Q_{16}$, $D_{24}$, $\GL(2,3)$, $C_2.S_4$, $C_3\times Q_{16}$, $C_3\times D_8$

Order 42: $C_{42}$ x 11, $C_3\times D_7$ x 2, $S_3\times C_7$ x 2

Order 39: $C_{13}:C_3$ x 2, $C_{39}$

Order 36: $C_3\times C_{12}$ x 3, $C_3:C_{12}$ x 2, $C_6\times S_3$ x 2, $C_6^2$

Order 32: $\OD_{16}:C_2$ x 2, $C_4\wr C_2$ x 2, $D_8:C_2$, $C_4\times C_8$, $C_8.C_4$

Order 28: $C_{28}$ x 8, $C_2\times C_{14}$ x 4, $D_{14}$ x 2, $C_7:C_4$ x 2

Order 26: $C_{26}$, $D_{13}$

Order 24: $C_{24}$ x 13, $C_2\times C_{12}$ x 7, $C_3\times D_4$ x 3, $C_3:D_4$ x 2, $D_{12}$ x 2, $C_4\times S_3$ x 2, $C_3:Q_8$ x 2, $\SL(2,3)$ x 2, $C_3\times Q_8$ x 2, $C_3:C_8$ x 2

Order 21: $C_{21}$ x 5

Order 18: $C_3\times C_6$ x 2, $C_3\times S_3$ x 2

Order 16: $\OD_{16}$ x 3, $C_2\times C_8$ x 3, $\SD_{16}$ x 2, $D_4:C_2$ x 2, $Q_{16}$, $D_8$, $C_4^2$

Order 14: $C_{14}$ x 7, $D_7$ x 2

Order 13: $C_{13}$

Order 12: $C_{12}$ x 10, $C_2\times C_6$ x 4, $D_6$ x 2, $C_3:C_4$ x 2

Order 9: $C_3^2$

Order 8: $C_8$ x 5, $D_4$ x 3, $C_2\times C_4$ x 3, $Q_8$ x 2

Order 7: $C_7$ x 3

Order 6: $C_6$ x 7, $S_3$ x 2

Order 4: $C_4$ x 4, $C_2^2$ x 2

Order 3: $C_3$ x 3

Order 2: $C_2$ x 3

Order 1: $C_1$

Normal subgroups (quotient in parentheses)

Order 366912: $\GUnitary(2,13)$ ($C_1$)

Order 183456: $C_{168}.\PSL(2,13)$ ($C_2$), $C_{84}.\PSL(2,13).C_2$ ($C_2$), $C_{84}.\PSL(2,13).C_2$ ($C_2$)

Order 122304: $C_{56}.\PSL(2,13).C_2$ ($C_3$)

Order 91728: $C_{42}.\PSL(2,13).C_2$ ($C_4$), $C_{42}.\PSL(2,13).C_2$ ($C_4$), $C_{84}.\PSL(2,13)$ ($C_2^2$)

Order 61152: $C_{28}.\PSL(2,13).C_2$ ($C_6$), $C_{56}.\PSL(2,13)$ ($C_6$), $C_{28}.\PSL(2,13).C_2$ ($C_6$)

Order 52416: $C_{24}.\PSL(2,13).C_2$ ($C_7$)

Order 45864: $C_{42}.\PSL(2,13)$ ($C_2\times C_4$)

Order 30576: $C_{14}.\PSL(2,13).C_2$ ($C_{12}$), $C_{28}.\PSL(2,13)$ ($C_2\times C_6$), $C_{14}.\PSL(2,13).C_2$ ($C_{12}$)

Order 26208: $C_{24}.\PSL(2,13)$ ($C_{14}$), $C_{12}.\PSL(2,13).C_2$ ($C_{14}$), $C_{12}.\PSL(2,13).C_2$ ($C_{14}$)

Order 17472: $C_8.\PSL(2,13).C_2$ ($C_{21}$)

Order 15288: $C_{14}.\PSL(2,13)$ ($C_2\times C_{12}$)

Order 13104: $C_6.\PSL(2,13).C_2$ ($C_{28}$), $C_6.\PSL(2,13).C_2$ ($C_{28}$), $C_{12}.\PSL(2,13)$ ($C_2\times C_{14}$)

Order 8736: $C_4.\PSL(2,13).C_2$ ($C_{42}$), $C_8.\PSL(2,13)$ ($C_{42}$), $C_4.\PSL(2,13).C_2$ ($C_{42}$)

Order 6552: $C_6.\PSL(2,13)$ ($C_2\times C_{28}$)

Order 4368: $C_2.\PSL(2,13).C_2$ ($C_{84}$), $C_4.\PSL(2,13)$ ($C_2\times C_{42}$), $C_2.\PSL(2,13).C_2$ ($C_{84}$)

Order 2184: $C_2.\PSL(2,13)$ ($C_2\times C_{84}$)

Order 168: $C_{168}$ ($\PSL(2,13).C_2$)

Order 84: $C_{84}$ ($C_2\times \PSL(2,13).C_2$)

Order 56: $C_{56}$ ($C_3\times \PSL(2,13).C_2$)

Order 42: $C_{42}$ ($C_4\times \PSL(2,13).C_2$)

Order 28: $C_{28}$ ($C_6\times \PSL(2,13).C_2$)

Order 24: $C_{24}$ ($C_7.\PSL(2,13).C_2$)

Order 21: $C_{21}$ ($C_8.\PSL(2,13).C_2$)

Order 14: $C_{14}$ ($C_{12}\times \PSL(2,13).C_2$)

Order 12: $C_{12}$ ($C_{14}.\PSL(2,13).C_2$)

Order 8: $C_8$ ($C_{21}.\PSL(2,13).C_2$)

Order 7: $C_7$ ($C_{24}.\PSL(2,13).C_2$)

Order 6: $C_6$ ($C_{28}.\PSL(2,13).C_2$)

Order 4: $C_4$ ($C_{42}.\PSL(2,13).C_2$)

Order 3: $C_3$ ($C_{56}.\PSL(2,13).C_2$)

Order 2: $C_2$ ($C_{84}.\PSL(2,13).C_2$)

Order 1: $C_1$ ($\GUnitary(2,13)$)

Normal subgroups up to automorphism (quotient in parentheses)

Order 366912: $\GUnitary(2,13)$ ($C_1$)

Order 183456: $C_{168}.\PSL(2,13)$ ($C_2$), $C_{84}.\PSL(2,13).C_2$ ($C_2$), $C_{84}.\PSL(2,13).C_2$ ($C_2$)

Order 122304: $C_{56}.\PSL(2,13).C_2$ ($C_3$)

Order 91728: $C_{42}.\PSL(2,13).C_2$ ($C_4$), $C_{42}.\PSL(2,13).C_2$ ($C_4$), $C_{84}.\PSL(2,13)$ ($C_2^2$)

Order 61152: $C_{28}.\PSL(2,13).C_2$ ($C_6$), $C_{56}.\PSL(2,13)$ ($C_6$), $C_{28}.\PSL(2,13).C_2$ ($C_6$)

Order 52416: $C_{24}.\PSL(2,13).C_2$ ($C_7$)

Order 45864: $C_{42}.\PSL(2,13)$ ($C_2\times C_4$)

Order 30576: $C_{14}.\PSL(2,13).C_2$ ($C_{12}$), $C_{28}.\PSL(2,13)$ ($C_2\times C_6$), $C_{14}.\PSL(2,13).C_2$ ($C_{12}$)

Order 26208: $C_{24}.\PSL(2,13)$ ($C_{14}$), $C_{12}.\PSL(2,13).C_2$ ($C_{14}$), $C_{12}.\PSL(2,13).C_2$ ($C_{14}$)

Order 17472: $C_8.\PSL(2,13).C_2$ ($C_{21}$)

Order 15288: $C_{14}.\PSL(2,13)$ ($C_2\times C_{12}$)

Order 13104: $C_6.\PSL(2,13).C_2$ ($C_{28}$), $C_6.\PSL(2,13).C_2$ ($C_{28}$), $C_{12}.\PSL(2,13)$ ($C_2\times C_{14}$)

Order 8736: $C_4.\PSL(2,13).C_2$ ($C_{42}$), $C_8.\PSL(2,13)$ ($C_{42}$), $C_4.\PSL(2,13).C_2$ ($C_{42}$)

Order 6552: $C_6.\PSL(2,13)$ ($C_2\times C_{28}$)

Order 4368: $C_2.\PSL(2,13).C_2$ ($C_{84}$), $C_4.\PSL(2,13)$ ($C_2\times C_{42}$), $C_2.\PSL(2,13).C_2$ ($C_{84}$)

Order 2184: $C_2.\PSL(2,13)$ ($C_2\times C_{84}$)

Order 168: $C_{168}$ ($\PSL(2,13).C_2$)

Order 84: $C_{84}$ ($C_2\times \PSL(2,13).C_2$)

Order 56: $C_{56}$ ($C_3\times \PSL(2,13).C_2$)

Order 42: $C_{42}$ ($C_4\times \PSL(2,13).C_2$)

Order 28: $C_{28}$ ($C_6\times \PSL(2,13).C_2$)

Order 24: $C_{24}$ ($C_7.\PSL(2,13).C_2$)

Order 21: $C_{21}$ ($C_8.\PSL(2,13).C_2$)

Order 14: $C_{14}$ ($C_{12}\times \PSL(2,13).C_2$)

Order 12: $C_{12}$ ($C_{14}.\PSL(2,13).C_2$)

Order 8: $C_8$ ($C_{21}.\PSL(2,13).C_2$)

Order 7: $C_7$ ($C_{24}.\PSL(2,13).C_2$)

Order 6: $C_6$ ($C_{28}.\PSL(2,13).C_2$)

Order 4: $C_4$ ($C_{42}.\PSL(2,13).C_2$)

Order 3: $C_3$ ($C_{56}.\PSL(2,13).C_2$)

Order 2: $C_2$ ($C_{84}.\PSL(2,13).C_2$)

Order 1: $C_1$ ($\GUnitary(2,13)$)

Series

Derived series

$\GUnitary(2,13)$

$\rhd$

$C_2.\PSL(2,13)$

Chief series

$\GUnitary(2,13)$

$\rhd$

$C_{168}.\PSL(2,13)$

$\rhd$

$C_{168}$

$\rhd$

$C_{84}$

$\rhd$

$C_{42}$

$\rhd$

$C_{21}$

$\rhd$

$C_7$

$\rhd$

$C_1$

Lower central series

$\GUnitary(2,13)$

$\rhd$

$C_2.\PSL(2,13)$

Upper central series

$C_1$

$\lhd$

$C_{168}$

Character theory

Complex character table

The $2352 \times 2352$ character table is not available for this group.

Rational character table

The $184 \times 184$ rational character table is not available for this group.