Abstract group 3456.ke: $(C_2\times D_6^2):A_4$

• Label: 3456.ke
• Order: \( 2^{7} \cdot 3^{3} \)
• Exponent: \( 2^{2} \cdot 3 \)
• Nilpotent: no
• Solvable: yes
• $\card{G^{\mathrm{ab}}}$: \( 2^{2} \cdot 3 \)
• $\card{Z(G)}$: \( 2 \)
• $\card{\Aut(G)}$: \( 2^{11} \cdot 3^{3} \)
• $\card{\mathrm{Out}(G)}$: \( 2^{5} \)
• Perm deg.: $14$
• Trans deg.: $48$
• Rank: $2$

Group information

Description:	$(C_2\times D_6^2):A_4$
Order:	\(3456\)\(\medspace = 2^{7} \cdot 3^{3} \)
Exponent:	\(12\)\(\medspace = 2^{2} \cdot 3 \)
Automorphism group:	$C_6^2.(C_2^4\times A_4).C_2^3$, of order \(55296\)\(\medspace = 2^{11} \cdot 3^{3} \)
Composition factors:	$C_2$ x 7, $C_3$ x 3
Derived length:	$3$

This group is nonabelian and monomial (hence solvable).

Group statistics

Order	1	2	3	4	6	12
Elements	1	247	296	264	2264	384	3456
Conjugacy classes	1	11	11	4	42	6	75
Divisions	1	11	7	4	28	6	57
Autjugacy classes	1	7	5	3	13	3	32

Dimension	1	2	3	4	6	8	12	16	32
Irr. complex chars.	12	12	4	15	8	12	9	3	0	75
Irr. rational chars.	4	8	4	9	8	9	9	5	1	57

Minimal presentations

Permutation degree:	$14$
Transitive degree:	$48$
Rank:	$2$
Inequivalent generating pairs:	$24$

Minimal degrees of faithful linear representations

	Over $\mathbb{C}$	Over $\mathbb{R}$	Over $\mathbb{Q}$
Irreducible	16	16	16
Arbitrary	not computed	not computed	not computed

Constructions

Presentation:	${\langle a, b, c, d, e \mid a^{6}=b^{2}=c^{4}=d^{6}=e^{12}=[b,e]=[d,e]=1, b^{a}= \!\cdots\! \rangle}$
Permutation group:	Degree $14$ $\langle(8,13)(9,12), (1,6)(2,3)(4,5)(7,11,14,10)(8,12)(9,13), (7,10)(8,12)(9,13) \!\cdots\! \rangle$
Direct product:	not isomorphic to a non-trivial direct product
Semidirect product:	$(Q_8:A_4)$ $\,\rtimes\,$ $S_3^2$	$(C_2\times D_6^2)$ $\,\rtimes\,$ $A_4$	$(C_3\times Q_8:A_4)$ $\,\rtimes\,$ $D_6$ (2)	$C_3^2$ $\,\rtimes\,$ $(C_2^5:A_4)$	all 17
Trans. wreath product:	not isomorphic to a non-trivial transitive wreath product
Non-split product:	$C_2$ . $(D_6^2:A_4)$	$C_2^3$ . $(A_4\times S_3^2)$	$C_6$ . $(S_3\times C_2^3:A_4)$ (2)	$(C_6:S_3)$ . $(C_2^3:A_4)$	all 8

Elements of the group are displayed as permutations of degree 14.

Homology

Abelianization:	$C_{2} \times C_{6} \simeq C_{2}^{2} \times C_{3}$
Schur multiplier:	$C_{2}^{3}$
Commutator length:	$1$

Subgroups

There are 26778 subgroups in 1247 conjugacy classes, 41 normal (17 characteristic).

Characteristic subgroups are shown in this color. Normal (but not characteristic) subgroups are shown in this color.

Special subgroups

Center:	$Z \simeq$ $C_2$	$G/Z \simeq$ $D_6^2:A_4$
Commutator:	$G' \simeq$ $D_4:C_6^2$	$G/G' \simeq$ $C_2\times C_6$
Frattini:	$\Phi \simeq$ $C_2^3$	$G/\Phi \simeq$ $A_4\times S_3^2$
Fitting:	$\operatorname{Fit} \simeq$ $D_4:C_6^2$	$G/\operatorname{Fit} \simeq$ $C_2\times C_6$
Radical:	$R \simeq$ $(C_2\times D_6^2):A_4$	$G/R \simeq$ $C_1$
Socle:	$\operatorname{soc} \simeq$ $C_3\times C_6$	$G/\operatorname{soc} \simeq$ $C_2^4:A_4$
2-Sylow subgroup:	$P_{ 2 } \simeq$ $C_2^4:D_4$
3-Sylow subgroup:	$P_{ 3 } \simeq$ $C_3^3$

Hi

Subgroup diagram and profile

Classes of subgroups up to conjugation

No diagram available

Classes of subgroups up to automorphism

No diagram available

Normal subgroups

No diagram available

Normal subgroups up to automorphism

No diagram available

Classes of subgroups up to conjugation

Order 3456: $(C_2\times D_6^2):A_4$

Order 1728: $C_3^2:C_2\wr A_4$ x 2, $D_4:C_6^2:C_6$

Order 1152: $(C_3\times C_2^3:A_4).C_2^2$ x 2, $C_6^2.C_2^4.C_2$

Order 864: $D_6^2:C_6$, $C_3^2\times Q_8:A_4$

Order 576: $(C_2^2\times D_6):A_4$ x 4, $S_3\times Q_8:A_4$ x 3, $(C_6\times C_{12}):D_4$ x 2, $C_3\times C_2\wr A_4$ x 2, $(C_2\times C_{12}):D_{12}$ x 2, $C_6^2.C_2^4$, $D_6^2:C_2^2$, $(C_6\times D_4).D_6$

Order 432: $A_4\times S_3^2$ x 4, $C_6:S_3\times A_4$ x 2, $C_6\times S_3\times A_4$ x 2, $C_3:S_3\times \SL(2,3)$

Order 384: $C_2\wr C_2^2\times S_3$ x 2, $C_2^5:A_4$

Order 288: $C_3\times Q_8:A_4$ x 6, $C_6^2:D_4$ x 2, $C_6^2:D_4$ x 2, $C_6^2.D_4$ x 2, $C_6^2.D_4$ x 2, $C_2\times A_4\times D_6$ x 2, $C_6^2.C_2^3$ x 2, $C_6^2:C_2^3$ x 2, $D_6^2:C_2$, $D_6^2:C_2$, $C_2^3.S_3^2$, $D_6:D_{12}$, $D_6^2.C_2$, $C_2\times D_6^2$, $D_4:C_6^2$, $C_6^2.C_2^3$, $C_6^2.C_2^3$

Order 216: $C_6^2:C_6$ x 4, $C_6^2:C_6$ x 4, $C_6^2:C_6$ x 2, $C_6\times S_3^2$, $C_3^2\times \SL(2,3)$

Order 192: $C_2\wr A_4$ x 4, $D_{12}:C_2^3$ x 3, $C_3\times C_2\wr C_2^2$ x 2, $(C_2\times C_{12}):D_4$ x 2, $C_2^4:D_6$ x 2, $C_2^3:C_4\times S_3$ x 2, $C_2^3:D_{12}$ x 2, $C_2^4:D_6$ x 2, $C_2^4:A_4$

Order 144: $A_4\times D_6$ x 19, $C_{12}:D_6$ x 9, $D_6^2$ x 6, $C_6^2:C_2^2$ x 4, $D_6:D_6$ x 4, $S_3\times \SL(2,3)$ x 4, $C_6^2:C_2^2$ x 3, $C_{12}.D_6$ x 3, $C_{12}.D_6$ x 3, $C_6^2:C_4$ x 2, $D_6:C_{12}$ x 2, $C_6.D_{12}$ x 2, $C_6^2:C_2^2$ x 2, $C_2^2:C_6^2$ x 2, $C_4:C_6^2$ x 2, $C_6:D_{12}$ x 2, $C_{12}:D_6$ x 2, $C_6^2:C_2^2$ x 2, $C_6:D_{12}$ x 2, $C_6.D_{12}$, $C_4.C_6^2$, $C_{12}.D_6$, $C_{12}.D_6$, $C_2^2.S_3^2$

Order 128: $C_2^4:D_4$

Order 108: $C_3\times S_3^2$ x 4, $C_3^2\times D_6$ x 2, $C_3^2\times A_4$ x 2, $C_3^2:D_6$

Order 96: $D_4\times D_6$ x 9, $D_4:D_6$ x 7, $C_2^2:D_{12}$ x 4, $D_6.D_4$ x 4, $D_4:D_6$ x 4, $D_4:D_6$ x 4, $Q_8:A_4$ x 4, $D_6:D_4$ x 4, $C_2^2.D_{12}$ x 4, $C_6.C_2^4$ x 3, $C_2^3:C_{12}$ x 2, $C_2^3.D_6$ x 2, $C_2^3\times D_6$ x 2, $C_2^4:C_6$ x 2, $C_2^4:S_3$ x 2, $C_2^3\times A_4$

Order 72: $S_3\times A_4$ x 22, $C_6\times A_4$ x 18, $C_6:D_6$ x 12, $S_3\times D_6$ x 12, $C_6\times D_6$ x 8, $C_3\times \SL(2,3)$ x 8, $C_6^2:C_2$ x 6, $C_{12}:S_3$ x 4, $C_6\wr C_2$ x 4, $C_3:D_{12}$ x 4, $C_2\times C_6^2$ x 3, $D_4\times C_3^2$ x 3, $C_3:D_{12}$ x 3, $C_6\times C_{12}$ x 2, $C_6.D_6$ x 2, $C_6:C_{12}$ x 2, $C_6.D_6$ x 2, $Q_8\times C_3^2$, $C_3^2:Q_8$

Order 64: $C_2\wr C_2^2$ x 4, $C_2^4:C_4$, $D_4:C_2^3$, $C_2^3:D_4$

Order 54: $S_3\times C_3^2$ x 4, $C_3^2:C_6$ x 2, $C_3^2\times C_6$

Order 48: $S_3\times D_4$ x 44, $C_2^2\times D_6$ x 24, $C_6:D_4$ x 18, $D_4:S_3$ x 12, $D_{12}:C_2$ x 12, $C_2^2\times A_4$ x 10, $C_6\times D_4$ x 9, $C_2\times D_{12}$ x 9, $C_4\times D_6$ x 9, $D_6:C_4$ x 6, $D_4:C_6$ x 4, $D_{12}:C_2$ x 4, $S_3\times Q_8$ x 4, $C_2^2:C_{12}$ x 4, $C_6.D_4$ x 4, $C_2^3\times C_6$ x 2, $C_2\times \SL(2,3)$

Order 36: $C_6\times S_3$ x 23, $C_3\times A_4$ x 14, $C_6:S_3$ x 11, $S_3^2$ x 8, $C_6^2$ x 7, $C_3:C_{12}$ x 2, $C_3\times C_{12}$, $C_3^2:C_4$

Order 32: $C_2^2\wr C_2$ x 6, $C_2^3:C_4$ x 4, $D_4:C_2^2$ x 4, $C_2^2\times D_4$ x 3, $C_2^3:C_4$ x 2, $C_2^5$, $D_4:C_2^2$

Order 27: $C_3^3$

Order 24: $C_2\times D_6$ x 71, $C_3:D_4$ x 32, $C_2\times A_4$ x 21, $C_4\times S_3$ x 20, $C_2^2\times C_6$ x 17, $D_{12}$ x 16, $C_3\times D_4$ x 16, $C_2\times C_{12}$ x 9, $C_6:C_4$ x 9, $\SL(2,3)$ x 5, $C_3:Q_8$ x 4, $C_3\times Q_8$ x 4

Order 18: $C_3\times S_3$ x 18, $C_3\times C_6$ x 13, $C_3:S_3$ x 4

Order 16: $C_2\times D_4$ x 25, $C_2^4$ x 11, $D_4:C_2$ x 8, $C_2^2:C_4$ x 7, $C_2^2\times C_4$ x 3, $C_2\times Q_8$

Order 12: $D_6$ x 62, $C_2\times C_6$ x 34, $A_4$ x 9, $C_{12}$ x 6, $C_3:C_4$ x 6

Order 9: $C_3^2$ x 7

Order 8: $C_2^3$ x 33, $D_4$ x 20, $C_2\times C_4$ x 12, $Q_8$ x 2

Order 6: $C_6$ x 28, $S_3$ x 17

Order 4: $C_2^2$ x 32, $C_4$ x 4

Order 3: $C_3$ x 7

Order 2: $C_2$ x 11

Order 1: $C_1$

Classes of subgroups up to automorphism

Order 3456: $(C_2\times D_6^2):A_4$

Order 1728: $D_4:C_6^2:C_6$, $C_3^2:C_2\wr A_4$

Order 1152: $(C_3\times C_2^3:A_4).C_2^2$, $C_6^2.C_2^4.C_2$

Order 864: $D_6^2:C_6$, $C_3^2\times Q_8:A_4$

Order 576: $S_3\times Q_8:A_4$ x 2, $(C_2^2\times D_6):A_4$ x 2, $C_6^2.C_2^4$, $D_6^2:C_2^2$, $(C_6\times C_{12}):D_4$, $C_3\times C_2\wr A_4$, $(C_2\times C_{12}):D_{12}$, $(C_6\times D_4).D_6$

Order 432: $C_6:S_3\times A_4$ x 2, $C_6\times S_3\times A_4$, $A_4\times S_3^2$, $C_3:S_3\times \SL(2,3)$

Order 384: $C_2^5:A_4$, $C_2\wr C_2^2\times S_3$

Order 288: $C_3\times Q_8:A_4$ x 4, $C_6^2.C_2^3$ x 2, $C_6^2:C_2^3$ x 2, $D_6^2:C_2$, $C_6^2:D_4$, $D_6^2:C_2$, $C_6^2:D_4$, $C_2^3.S_3^2$, $D_6:D_{12}$, $D_6^2.C_2$, $C_6^2.D_4$, $C_6^2.D_4$, $C_2\times D_6^2$, $C_2\times A_4\times D_6$, $D_4:C_6^2$, $C_6^2.C_2^3$, $C_6^2.C_2^3$

Order 216: $C_6^2:C_6$ x 2, $C_6^2:C_6$ x 2, $C_6\times S_3^2$, $C_6^2:C_6$, $C_3^2\times \SL(2,3)$

Order 192: $C_2\wr A_4$ x 2, $D_{12}:C_2^3$ x 2, $C_3\times C_2\wr C_2^2$, $(C_2\times C_{12}):D_4$, $C_2^4:D_6$, $C_2^3:C_4\times S_3$, $C_2^3:D_{12}$, $C_2^4:A_4$, $C_2^4:D_6$

Order 144: $A_4\times D_6$ x 7, $C_{12}:D_6$ x 5, $C_6^2:C_2^2$ x 4, $C_6^2:C_2^2$ x 3, $D_6^2$ x 3, $C_4:C_6^2$ x 2, $C_{12}.D_6$ x 2, $C_{12}.D_6$ x 2, $C_6:D_{12}$ x 2, $C_{12}:D_6$ x 2, $S_3\times \SL(2,3)$ x 2, $C_6^2:C_4$, $D_6:C_{12}$, $C_6.D_{12}$, $C_6.D_{12}$, $C_6^2:C_2^2$, $C_2^2:C_6^2$, $C_4.C_6^2$, $C_{12}.D_6$, $C_{12}.D_6$, $C_6^2:C_2^2$, $D_6:D_6$, $C_6:D_{12}$, $C_2^2.S_3^2$

Order 128: $C_2^4:D_4$

Order 108: $C_3^2\times A_4$ x 2, $C_3^2:D_6$, $C_3^2\times D_6$, $C_3\times S_3^2$

Order 96: $D_4\times D_6$ x 5, $D_4:D_6$ x 4, $Q_8:A_4$ x 3, $C_2^2:D_{12}$ x 2, $D_6.D_4$ x 2, $C_6.C_2^4$ x 2, $D_4:D_6$ x 2, $D_4:D_6$ x 2, $D_6:D_4$ x 2, $C_2^3:C_{12}$, $C_2^3.D_6$, $C_2^3\times D_6$, $C_2^3\times A_4$, $C_2^4:C_6$, $C_2^4:S_3$, $C_2^2.D_{12}$

Order 72: $C_6:D_6$ x 9, $C_6\times A_4$ x 9, $S_3\times A_4$ x 6, $S_3\times D_6$ x 5, $C_3\times \SL(2,3)$ x 4, $C_2\times C_6^2$ x 3, $C_6\times D_6$ x 3, $C_6^2:C_2$ x 3, $C_{12}:S_3$ x 3, $D_4\times C_3^2$ x 2, $C_6\times C_{12}$ x 2, $C_6.D_6$ x 2, $C_3:D_{12}$ x 2, $Q_8\times C_3^2$, $C_3^2:Q_8$, $C_6\wr C_2$, $C_6:C_{12}$, $C_3:D_{12}$, $C_6.D_6$

Order 64: $C_2\wr C_2^2$ x 2, $C_2^4:C_4$, $D_4:C_2^3$, $C_2^3:D_4$

Order 54: $C_3^2\times C_6$, $C_3^2:C_6$, $S_3\times C_3^2$

Order 48: $S_3\times D_4$ x 11, $C_2^2\times D_6$ x 10, $C_6:D_4$ x 10, $C_2^2\times A_4$ x 5, $C_6\times D_4$ x 5, $C_2\times D_{12}$ x 5, $C_4\times D_6$ x 5, $D_4:S_3$ x 4, $D_{12}:C_2$ x 4, $D_6:C_4$ x 3, $D_4:C_6$ x 2, $D_{12}:C_2$ x 2, $S_3\times Q_8$ x 2, $C_2^2:C_{12}$ x 2, $C_6.D_4$ x 2, $C_2^3\times C_6$, $C_2\times \SL(2,3)$

Order 36: $C_6:S_3$ x 9, $C_6\times S_3$ x 8, $C_3\times A_4$ x 8, $C_6^2$ x 6, $S_3^2$ x 2, $C_3\times C_{12}$, $C_3^2:C_4$, $C_3:C_{12}$

Order 32: $D_4:C_2^2$ x 4, $C_2^2\wr C_2$ x 4, $C_2^2\times D_4$ x 3, $C_2^3:C_4$ x 2, $C_2^3:C_4$ x 2, $C_2^5$, $D_4:C_2^2$

Order 27: $C_3^3$

Order 24: $C_2\times D_6$ x 26, $C_2\times A_4$ x 10, $C_2^2\times C_6$ x 9, $C_3:D_4$ x 8, $C_4\times S_3$ x 7, $C_2\times C_{12}$ x 5, $C_6:C_4$ x 5, $D_{12}$ x 5, $C_3\times D_4$ x 5, $\SL(2,3)$ x 3, $C_3:Q_8$ x 2, $C_3\times Q_8$ x 2

Order 18: $C_3\times C_6$ x 8, $C_3\times S_3$ x 5, $C_3:S_3$ x 3

Order 16: $C_2\times D_4$ x 16, $C_2^4$ x 7, $D_4:C_2$ x 6, $C_2^2:C_4$ x 4, $C_2^2\times C_4$ x 3, $C_2\times Q_8$

Order 12: $D_6$ x 23, $C_2\times C_6$ x 17, $A_4$ x 6, $C_{12}$ x 3, $C_3:C_4$ x 3

Order 9: $C_3^2$ x 5

Order 8: $C_2^3$ x 19, $D_4$ x 9, $C_2\times C_4$ x 9, $Q_8$ x 2

Order 6: $C_6$ x 13, $S_3$ x 7

Order 4: $C_2^2$ x 19, $C_4$ x 3

Order 3: $C_3$ x 5

Order 2: $C_2$ x 7

Order 1: $C_1$

Normal subgroups (quotient in parentheses)

Order 3456: $(C_2\times D_6^2):A_4$ ($C_1$)

Order 1728: $C_3^2:C_2\wr A_4$ ($C_2$) x 2, $D_4:C_6^2:C_6$ ($C_2$)

Order 1152: $C_6^2.C_2^4.C_2$ ($C_3$)

Order 864: $C_3^2\times Q_8:A_4$ ($C_2^2$)

Order 576: $(C_6\times C_{12}):D_4$ ($C_6$) x 2, $(C_2^2\times D_6):A_4$ ($S_3$) x 2, $C_6^2.C_2^4$ ($C_6$)

Order 288: $C_3\times Q_8:A_4$ ($D_6$) x 2, $C_2\times D_6^2$ ($A_4$), $D_4:C_6^2$ ($C_2\times C_6$)

Order 192: $(C_2\times C_{12}):D_4$ ($C_3\times S_3$) x 2

Order 144: $C_6^2:C_2^2$ ($C_2\times A_4$) x 2, $C_6^2:C_2^2$ ($C_2\times A_4$)

Order 96: $C_6.C_2^4$ ($C_6\times S_3$) x 2, $Q_8:A_4$ ($S_3^2$)

Order 72: $C_2\times C_6^2$ ($C_2^2\times A_4$)

Order 48: $C_2^2\times D_6$ ($S_3\times A_4$) x 2

Order 36: $C_6:S_3$ ($C_2^3:A_4$)

Order 32: $D_4:C_2^2$ ($C_3\times S_3^2$)

Order 24: $C_2^2\times C_6$ ($A_4\times D_6$) x 2

Order 18: $C_3:S_3$ ($C_2\wr A_4$) x 2, $C_3\times C_6$ ($C_2^4:A_4$)

Order 9: $C_3^2$ ($C_2^5:A_4$)

Order 8: $C_2^3$ ($A_4\times S_3^2$)

Order 6: $C_6$ ($S_3\times C_2^3:A_4$) x 2

Order 3: $C_3$ ($C_6.C_2^2\wr C_2:C_3.C_2$), $C_3$ ($(C_3\times C_2^3:A_4).C_2^2$)

Order 2: $C_2$ ($D_6^2:A_4$)

Order 1: $C_1$ ($(C_2\times D_6^2):A_4$)

Normal subgroups up to automorphism (quotient in parentheses)

Order 3456: $(C_2\times D_6^2):A_4$ ($C_1$)

Order 1728: $D_4:C_6^2:C_6$ ($C_2$), $C_3^2:C_2\wr A_4$ ($C_2$)

Order 1152: $C_6^2.C_2^4.C_2$ ($C_3$)

Order 864: $C_3^2\times Q_8:A_4$ ($C_2^2$)

Order 576: $C_6^2.C_2^4$ ($C_6$), $(C_6\times C_{12}):D_4$ ($C_6$), $(C_2^2\times D_6):A_4$ ($S_3$)

Order 288: $C_3\times Q_8:A_4$ ($D_6$), $C_2\times D_6^2$ ($A_4$), $D_4:C_6^2$ ($C_2\times C_6$)

Order 192: $(C_2\times C_{12}):D_4$ ($C_3\times S_3$)

Order 144: $C_6^2:C_2^2$ ($C_2\times A_4$), $C_6^2:C_2^2$ ($C_2\times A_4$)

Order 96: $C_6.C_2^4$ ($C_6\times S_3$), $Q_8:A_4$ ($S_3^2$)

Order 72: $C_2\times C_6^2$ ($C_2^2\times A_4$)

Order 48: $C_2^2\times D_6$ ($S_3\times A_4$)

Order 36: $C_6:S_3$ ($C_2^3:A_4$)

Order 32: $D_4:C_2^2$ ($C_3\times S_3^2$)

Order 24: $C_2^2\times C_6$ ($A_4\times D_6$)

Order 18: $C_3\times C_6$ ($C_2^4:A_4$), $C_3:S_3$ ($C_2\wr A_4$)

Order 9: $C_3^2$ ($C_2^5:A_4$)

Order 8: $C_2^3$ ($A_4\times S_3^2$)

Order 6: $C_6$ ($S_3\times C_2^3:A_4$)

Order 3: $C_3$ ($C_6.C_2^2\wr C_2:C_3.C_2$)

Order 2: $C_2$ ($D_6^2:A_4$)

Order 1: $C_1$ ($(C_2\times D_6^2):A_4$)

Series

Derived series

$(C_2\times D_6^2):A_4$

$\rhd$

$D_4:C_6^2$

$\rhd$

$C_2$

$\rhd$

$C_1$

Chief series

$(C_2\times D_6^2):A_4$

$\rhd$

$D_4:C_6^2:C_6$

$\rhd$

$C_3^2\times Q_8:A_4$

$\rhd$

$D_4:C_6^2$

$\rhd$

$C_2\times C_6^2$

$\rhd$

$C_3\times C_6$

$\rhd$

$C_6$

$\rhd$

$C_2$

$\rhd$

$C_1$

Lower central series

$(C_2\times D_6^2):A_4$

$\rhd$

$D_4:C_6^2$

Upper central series

$C_1$

$\lhd$

$C_2$

Supergroups

This group is a maximal subgroup of 7 larger groups in the database.

This group is a maximal quotient of 1 larger groups in the database.

Character theory

Complex character table

See the $75 \times 75$ character table. Alternatively, you may search for characters of this group with desired properties.

Rational character table

See the $57 \times 57$ rational character table.