Abstract group 501350400.a: $\ASigmaSp(4,4)$

• Label: 501350400.a
• Order: \( 2^{17} \cdot 3^{2} \cdot 5^{2} \cdot 17 \)
• Exponent: \( 2^{4} \cdot 3 \cdot 5 \cdot 17 \)
• Nilpotent: no
• Solvable: no
• $\card{G^{\mathrm{ab}}}$: \( 2 \)
• $\card{Z(G)}$: 1
• $\card{\Aut(G)}$: \( 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 17 \)
• $\card{\mathrm{Out}(G)}$: \( 2 \)
• Perm deg.: $256$
• Trans deg.: $256$
• Rank: $2$

Group information

Description:	$\ASigmaSp(4,4)$
Order:	\(501350400\)\(\medspace = 2^{17} \cdot 3^{2} \cdot 5^{2} \cdot 17 \)
Exponent:	\(4080\)\(\medspace = 2^{4} \cdot 3 \cdot 5 \cdot 17 \)
Automorphism group:	Group of order \(1002700800\)\(\medspace = 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 17 \)
Composition factors:	$C_2$ x 9, $\Sp(4,4)$
Derived length:	$1$

This group is nonabelian and nonsolvable.

Group statistics

Order	1	2	3	4	5	6	8	10	12	15	16	17	20	24
Elements	1	103615	1479680	13104960	11802624	44825600	61363200	83036160	88780800	66846720	31334400	58982400	18800640	20889600	501350400
Conjugacy classes	1	6	2	14	3	5	10	4	5	2	2	2	3	1	60
Divisions	1	6	2	14	3	5	9	4	5	2	1	1	2	1	56
Autjugacy classes	1	6	2	14	3	5	10	4	5	2	2	2	3	1	60

Dimension	1	18	34	36	50	85	102	153	255	256	340	408	450	510	900	1020	1275	1530	2550	3060	3825	5100	6120	7650	10200	12240
Irr. complex chars.	2	2	4	0	2	4	2	2	2	2	4	2	2	2	0	2	2	5	4	2	4	4	3	1	1	0	60
Irr. rational chars.	2	0	4	1	2	4	2	2	2	2	4	2	0	2	1	2	2	3	4	3	4	4	1	1	1	1	56

Minimal presentations

Permutation degree:	$256$
Transitive degree:	$256$
Rank:	$2$
Inequivalent generating pairs:	not computed

Minimal degrees of faithful linear representations

	Over $\mathbb{C}$	Over $\mathbb{R}$	Over $\mathbb{Q}$
Irreducible	255	255	255
Arbitrary	not computed	not computed	not computed

Constructions

Groups of Lie type:	$\ASigmaSp(4,4)$
Permutation group:	Degree $256$ $\langle(2,3,4)(5,9,13)(6,11,16)(7,12,14)(8,10,15)(17,49,33)(18,51,36)(19,52,34) \!\cdots\! \rangle$
Direct product:	not computed
Semidirect product:	not computed
Trans. wreath product:	not isomorphic to a non-trivial transitive wreath product
Possibly split product:	$C_2^8$ . $\PSigmaSp(4,4)$	$(C_2^8.\Sp(4,4))$ . $C_2$			more information

Elements of the group are displayed as permutations of degree 256.

Homology

Abelianization:	$C_{2} $
Schur multiplier:	$C_{2}$
Commutator length:	$1$

Subgroups

There are 4 normal subgroups, and all normal subgroups are characteristic.

Characteristic subgroups are shown in this color.

Special subgroups

Center:	a subgroup isomorphic to $C_1$
Commutator:	a subgroup isomorphic to $C_2^8.\Sp(4,4)$
Frattini:	a subgroup isomorphic to $C_1$
Fitting:	not computed
Radical:	not computed
Socle:	not computed
2-Sylow subgroup:	$P_{ 2 } \simeq$ $C_2^5.C_2^6.D_4^2$

Hi

Subgroup diagram and profile

Classes of subgroups up to conjugation

No diagram available: inclusions not computed

Classes of subgroups up to automorphism

No diagram available: inclusions not computed

Normal subgroups

No diagram available: inclusions not computed

Normal subgroups up to automorphism

No diagram available: inclusions not computed

Classes of subgroups up to conjugation

All subgroups of index up to 28800 (order at least 17408) are shown, as well as all normal subgroups of any index.

Order 501350400: $\ASigmaSp(4,4)$

Order 250675200: $C_2^8.\Sp(4,4)$

Order 5898240: $C_2^8.C_2^6.C_3.S_5$, $C_2^6.C_2^4.C_2^4.C_3.S_5$

Order 4177920: $C_2^8.\SL(2,16).C_4$, $\ASigmaL(2,16)$

Order 3686400: $C_2^8.A_5^2.C_2^2$, $C_2^8.\POPlus(4,5)$

Order 2949120: $C_2^{10}.C_2^4.C_3.A_5$, $C_2^8.C_2^6.C_3.A_5$

Order 2088960: $C_2^8.\SL(2,16).C_2$ x 2

Order 1966080: $C_2^8.C_2^6.S_5$ x 2

Order 1958400: $\PSigmaSp(4,4)$ x 2

Order 1843200: $C_2^8.A_5^2.C_2$ x 2, $C_2^8.A_5.S_5$ x 2, $C_2^8.\SOPlus(4,4)$ x 2

Order 1474560: $C_2^8.C_3.C_2^4.S_5$

Order 1179648: $C_2^8.C_2^6.A_4.S_3$

Order 1044480: $C_2^8.\SL(2,16)$, $C_2^8.\SL(2,16)$

Order 983040: $C_2^8.C_2^5.S_5$ x 2, $C_2^{10}.F_{16}.C_4$, $C_2^{10}.C_2^4.A_5$, $C_2^8.C_2^6.C_3:F_5$, $C_2^8.C_2^6.A_5$

Order 979200: $\Sp(4,4)$ x 3

Order 921600: $C_2^8.A_5.A_5$ x 2

Order 737280: $C_2^8.C_3.C_2^4.A_5$

Order 589824: $C_2^8.C_2^6.S_3^2$ x 2, $C_2^6.C_2^6.A_4^2$

Order 491520: $C_2^8.C_2^5.A_5$, $C_2^8.C_2^4.S_5$, $C_2^8.C_2^4.(D_5\times A_4)$, $C_2^6.C_2^4.C_5.C_2^4.C_6$

Order 393216: $C_2^6.C_2^6.A_4.D_4$ x 2, $C_2^8.C_2^6.S_4$, $C_2^8.C_2^6.D_6.C_2$

Order 368640: $C_4^2:A_4.C_2^4.S_5$, $C_2^{10}.C_3.S_5$, $C_2^6.C_2^4.C_3.S_5$, $C_2^5.C_2^4.A_6.C_2$

Order 327680: $C_2^8.C_2^4.C_2^2:F_5$, $C_2^6.C_2^4.C_5.C_2^3.C_2^3$

Order 307200: $C_2^8.D_5.S_5$, $C_2^4:D_5.C_2^4.S_5$

Order 294912: $C_2^8.C_2^6.C_3.C_6$ x 2, $C_2^{10}.A_4^2.C_2$, $C_2^8.C_2^4.(S_3\times A_4)$, $C_2^6.C_2^6.C_3:S_4$, $C_2^6.C_2^6.A_4.S_3$, $C_2^6.C_2^4.C_3.C_2^4.C_6$

Order 245760: $C_2^6.C_2^6.C_3:F_5$ x 2, $C_2^8.F_{16}.C_4$, $C_2^8.C_2^4.C_3:F_5$, $C_2^8.C_2^4.A_5$, $C_2^6.C_2^6.(C_5\times A_4)$, $C_2^6.C_2^4.F_{16}$

Order 196608: $C_2^8.C_2^6.C_6.C_2$ x 5, $C_2^8.C_2^6.D_6$ x 2, $C_2^6.C_2^6.A_4.C_2^2$ x 2, $C_2^8.C_2^6.A_4$, $C_2^8.C_2^4.D_6.C_2^2$, $C_2^6.C_2^4.C_6.C_2^4.C_2$

Order 184320: $C_2^8.A_6.C_2$ x 2, $C_4^2:A_4.C_2^4.A_5$, $C_2^{10}.C_3.A_5$, $C_2^8.C_2.A_6$, $C_2^6.C_2^4.C_3.A_5$, $C_2^2:S_4.C_2^4.S_5$, $C_2^8.(S_3\times S_5)$

Order 163840: $C_2^6.C_2^4.D_{10}.C_2^3$ x 6, $C_2^8.C_2^4.D_{10}.C_2$ x 3, $C_2^6.C_2^4.D_5.C_2^4$

Order 153600: $C_2^8.D_5.A_5$, $C_2^4:D_5.C_2^4.A_5$

Order 147456: $C_2^8.C_2^6.C_3^2$ x 3, $C_2^8.A_4\wr C_2.C_2$ x 2, $C_2^6.C_2^6.S_3^2$ x 2

Order 131072: $C_2^5.C_2^6.D_4^2$

Order 122880: $C_2^6.C_2^4.(D_5\times A_4)$ x 4, $C_2^8.C_2^2.S_5$ x 3, $C_2^6.C_2^4.S_5$ x 3, $C_2^{10}.S_5$, $C_2^8.F_{16}.C_2$, $C_2^{10}.S_5$

Order 115200: $C_2^4.A_5.S_5$ x 2

Order 102400: $C_2^8.(D_5^2.C_2^2)$

Order 98304: $C_2^8.C_2^4.D_6.C_2$ x 5, $C_2^8.C_2^6.S_3$ x 3, $C_2^6.C_2^6.D_6.C_2$ x 3, $C_2^6.C_2^4.D_6.C_2^3$ x 3, $C_2^6.C_2^4.C_2^3:D_6$ x 3, $C_2^6.C_2^4.C_2^2:D_{12}$ x 3, $C_2^6.C_2^6.A_4.C_2$ x 2, $C_2^6.C_2^4.C_6.C_2.C_2^3$ x 2, $C_2^6.C_2^4.C_2^4:S_3$ x 2, $C_2^6.C_2^4.C_2^4.S_3$ x 2, $C_2^9.C_2^4.C_6.C_2$, $C_2^8.C_6.C_2\wr C_2^2$, $C_2^8.C_4^2.S_4$, $C_2^8.C_2^6.C_6$, $C_2^8.C_2^4.D_{12}$, $C_2^7.C_2^4.D_6.C_2^2$, $C_2^6.C_2^6.S_4$, $C_2^6.C_2^6.C_6.C_2^2$, $C_2^6.C_2^4.C_6.C_2^3.C_2$, $C_2^5.C_2^6.S_4.C_2$, $C_2^5.C_2^6.C_6.C_2^3$, $C_2^4.C_2^6.D_6.C_2^3$

Order 92160: $C_2^8.C_3.S_5$ x 3, $C_2^4:C_3.C_2^4.S_5$ x 3, $C_4^2:C_3.C_2^4.S_5$, $C_2^8.A_6$, $C_2^2:S_4.C_2^4.A_5$, $C_2^8:(C_3\times S_5)$, $C_2^8.(S_3\times A_5)$

Order 81920: $C_2^6.C_2^4.C_2^2:F_5$ x 11, $C_2^6.C_2^4.D_5.C_2^3$ x 9, $C_2^6.C_2^4.C_5.C_2^4$ x 4, $C_2^8.C_2^4.F_5$ x 2, $C_2^8.C_2^4.D_{10}$ x 2, $C_2^8.C_2^4.C_{10}.C_2$, $C_2^2.C_2^4.C_2^4.C_2^2:F_5$

Order 76800: $C_2^8.C_5.A_5$, $C_2^4:C_5.C_2^4.A_5$

Order 73728: $C_2^6.C_2^6.C_3.S_3$ x 4, $C_2^6.C_2^4.(S_3\times A_4)$ x 4, $C_2^8.A_4^2.C_2$ x 3, $C_2^8.A_4\wr C_2$ x 2, $C_2^6.C_2^6.C_3.C_6$ x 2, $C_2^{10}.A_4.S_3$, $C_2^8.C_3.C_2^4.C_6$, $C_2^4.C_2^6.A_4.S_3$

Order 65536: $C_2.C_2^6.C_2^6.C_2^3$ x 2, $C_2^9.C_2^3.C_2^3.C_2$, $C_2^8.C_2^6.C_2^2$, $C_2^8.C_2^5.C_2^3$, $C_2^8.C_2^4.C_2^4$, $C_2^6.C_2^5.C_2.C_2^4$, $C_2^5.C_2^6.C_4.C_2^3$, $C_2^5.C_2^6.C_2^5$, $C_2^5.C_2^6.C_2^3.C_2^2$, $C_2^5.C_2^5.C_2^5.C_2$, $C_2^5.C_2^5.C_2^4.C_2^2$, $C_2^4.C_2^6.C_2^3.C_2^3$, $C_2^4.C_2^5.C_2^4.C_2^3$, $C_2^3.C_2^6.C_2^4.C_2^3$

Order 61440: $C_2^8.C_2.S_5$ x 6, $C_2^7.C_2^2.S_5$ x 5, $C_2^6.C_2^4.A_5$ x 4, $C_2^8.F_{16}$ x 3, $C_2^8.C_2^2.A_5$ x 3, $C_2^8:(C_2\times S_5)$ x 3, $C_2^6.C_2^6.C_{15}$ x 2, $C_2^3.C_2^6.S_5$ x 2, $C_2^{10}.A_5$, $C_2^6.F_{16}.C_4$, $C_2^6.C_2^4.C_3:F_5$, $C_2^5.C_2^4.S_5$, $C_2^4.C_2^6.C_3:F_5$, $C_2^{10}.A_5$, $C_2^6.F_{16}:C_4$, $C_2^8.(C_2\times S_5)$

Order 57600: $C_2^4.A_5.A_5$ x 3

Order 51200: $C_2^8:D_5:F_5$ x 2, $C_2^8.D_5\wr C_2$ x 2, $C_2^8.D_5:F_5$, $C_2^8.D_5\wr C_2$, $C_2^8.C_5^2:Q_8$

Order 49152: $C_2^6.C_2^4.D_6.C_2^2$ x 20, $C_2^8.C_2^4.D_6$ x 8, $C_2^7.C_2^4.D_6.C_2$ x 7, $C_2^6.C_2^4.C_6.C_2^3$ x 7, $C_2^8.C_2^4.C_6.C_2$ x 6, $C_2^6.C_2^6.C_6.C_2$ x 5, $C_2^6.C_2^4.D_6:C_4$ x 5, $C_2^7.C_2^4.C_6.C_2^2$ x 4, $C_2^6.C_2^6.D_6$ x 4, $C_2^6.C_2^4.(C_6.D_4)$ x 4, $C_2^4.C_2^6.D_6.C_2^2$ x 4, $C_2^8.C_2^6.C_3$ x 3, $C_2^4.C_2^6.C_6.C_2^3$ x 3, $C_2^8.C_3.C_2\wr C_4$ x 2, $C_2^8.A_4.C_2^4$ x 2, $C_2^8.A_4.C_2^3.C_2$ x 2, $C_2^8.(D_4\times S_4)$ x 2, $C_2^8.(C_2^5.S_3)$ x 2, $C_2^7.C_2^4.C_3.D_4$ x 2, $C_2^6.C_2^6.A_4$ x 2, $C_2^6.C_2^5.C_6.C_2^2$ x 2, $C_2^6.C_2^4.C_2^4.C_3$ x 2, $C_2^5.C_2^6.C_6.C_2^2$ x 2, $C_2^{10}.A_4.C_4$, $C_2^{10}.A_4.C_2^2$, $C_2^8.C_6.C_2^4.C_2$, $C_2^8.C_3.(D_4.D_4)$, $C_2^8.C_2^4:S_3.C_2$, $C_2^8.C_2^4.C_{12}$, $C_2^8.C_2^4.A_4$, $C_2^8.A_4.D_4.C_2$, $C_2^8.(C_4.D_4.S_3)$, $C_2^7.C_2^4.C_{12}.C_2$, $C_2^6.C_2^5.S_4$, $C_2^6.C_2^5.C_{12}.C_2$, $C_2^6.A_4.C_2^4.C_2^2$, $C_2^5.C_2^6.S_4$, $C_2^5.C_2^6.C_3.D_4$, $C_2^5.C_2^4.C_2^4.C_6$, $C_2^4.C_2^6.D_{12}.C_2$, $C_2^4.C_2^6.D_6:C_4$

Order 46080: $C_2^8.C_3.A_5$ x 4, $C_4^2:C_3.C_2^4.A_5$ x 2, $C_2^4:C_3.C_2^4.A_5$ x 2, $S_4.C_2^4.S_5$

Order 40960: $C_2^6.C_2^4.D_{10}.C_2$ x 37, $C_2^6.C_2^4.F_5.C_2$ x 5, $C_2^6.C_2^4.C_5.C_2^3$ x 4, $C_2^8.C_2^4.D_5$ x 2, $C_2^2.C_2^4.C_2^4.D_{10}.C_2$ x 2, $C_2^8.C_2^4.C_{10}$, $C_2^2.C_2^4.C_2^4.C_5.C_2^3$

Order 36864: $C_2^8.A_4^2$ x 6, $C_2^6.C_2^6.C_3^2$ x 6, $C_2^8.A_4.D_6$, $C_2^8.(S_3\times S_4)$, $C_2^6.A_4^2.C_2^2$, $C_2^6.A_4\wr C_2.C_2$, $C_2^6.\POPlus(4,3)$, $C_2^5.S_4\wr C_2$, $C_2^{10}.S_3^2$

Order 34816: $C_2^8.C_{17}:C_8$

Order 32768: $C_2^7.C_2^5.C_2^3$ x 11, $C_2^5.C_2^6.C_2^4$ x 9, $C_2^6.C_2^6.C_2^3$ x 8, $C_2^7.C_2.C_2^5.C_2^2$ x 7, $C_2.C_2^6.C_2^5.C_2^3$ x 7, $C_2^5.C_2^5.C_2.C_2^4$ x 6, $C_2^5.C_2^5.C_2^5$ x 5, $C_2^8.C_2^5.C_2^2$ x 3, $C_2^6.C_2^5.C_2^4$ x 3, $C_2.C_2^6.C_2^6.C_2^2$ x 3, $C_2^9.C_2^4.C_2^2$ x 2, $C_2^8.C_2^4.C_2^3$ x 2, $C_2^7.C_2^6.C_2^2$ x 2, $C_2^6.C_2^5.C_2^3.C_2$ x 2, $C_2^5.C_2^5.C_2^4.C_2$ x 2, $C_2^5.C_2^4.C_2^5.C_2$ x 2, $C_2^4.C_2^5.C_2^4.C_2^2$ x 2, $C_2^8.C_2^6.C_2$, $C_2^8.C_2.C_2^6$, $C_2^8.C_2.C_2^5.C_2$, $C_2^7.C_2^4.C_2^4$, $C_2^6.C_2^4.C_2^4.C_2$, $C_2^6.C_2.C_2^6.C_2^2$, $C_2^4.C_2^6.C_2^5$, $C_2^4.C_2^4.C_2^6.C_2$, $C_2^3.C_2^6.C_2^6$, $C_2^3.C_2^6.C_2^4.C_2^2$, $C_2^3.C_2^5.C_2^4.C_2^3$, $(C_2^4\times C_4).C_2^5.C_2^4$

Order 30720: $C_2^7.C_2.S_5$ x 11, $C_2^7.C_2^2.A_5$ x 7, $C_2^8.S_5$ x 6, $C_2^8:(C_2\times A_5)$ x 4, $C_2^8:S_5$ x 4, $C_2^8.C_2.A_5$ x 2, $C_2^6.C_2^3.A_5$ x 2, $C_2^6.C_2^2.S_5$ x 2, $C_2^3.C_2^6.A_5$ x 2, $Q_8.C_2^5.S_5$, $C_2^8.(S_3\times F_5)$, $C_2^8.(D_5\times A_4)$, $C_2^6.C_2^4.C_5.C_6$, $C_2^6.C_2^2:S_5$, $C_2^6.(D_5\times C_2^4:C_3)$, $(C_2^4\times C_4^2).S_5$, $C_2^8.(D_5\times A_4)$, $C_2^8.S_5$, $C_2^8.(S_3\times F_5)$, $C_2^8:(C_2\times A_5)$, $C_2^8.S_5$

Order 25600: $C_2^8.C_5.F_5$ x 2, $C_2^8.C_5:F_5$ x 2, $C_2^8.D_5^2$ x 2, $C_2^8.D_5^2$

Order 24576: $C_2^6.C_2^4.D_6.C_2$ x 43, $C_2^4.C_2^6.D_6.C_2$ x 17, $C_2^7.C_2^4.C_6.C_2$ x 13, $C_2^8.A_4.D_4$ x 12, $C_2^6.C_2^4.C_6.C_2^2$ x 12, $C_2^6.C_2^6.S_3$ x 11, $C_2^8.C_2^4.S_3$ x 10, $C_2^6.C_2^6.C_6$ x 10, $C_2^6.C_2^4.C_3.D_4$ x 10, $C_2^6.A_4.C_2^2\wr C_2$ x 10, $C_2^8.A_4.C_2^3$ x 8, $C_2^6.C_2^4.D_{12}$ x 8, $C_2^8.C_2^4.C_6$ x 7, $C_2^5.C_2^6.C_6.C_2$ x 7, $C_2^7.C_2^4.D_6$ x 6, $C_2^4.C_2^6.C_3.D_4$ x 5, $C_2^8.C_6.C_2^3.C_2$ x 4, $C_2^6.C_2^5.C_6.C_2$ x 3, $C_2^6.A_4.C_2^4.C_2$ x 3, $C_2^5.C_2^6.D_6$ x 3, $C_2^8.C_2^4:S_3$ x 2, $C_2^8.A_4.C_2^2.C_2$ x 2, $C_2^6.C_2^4.S_4$ x 2, $C_2^6.A_4.C_2^3.C_2^2$ x 2, $C_2^4.C_2^6.C_6.C_2^2$ x 2, $C_2^2.C_2^6.A_4.D_4$ x 2, $C_4^2.C_2^6.D_6.C_2$, $C_2^{10}.S_4$, $C_2^{10}.A_4.C_2$, $C_2^9.A_4.C_2^2$, $C_2^8.D_{12}:C_4$, $C_2^8.C_6.D_4.C_2$, $C_2^8.C_6.C_2^4$, $C_2^8.A_4.C_4.C_2$, $C_2^8.(C_6.D_4).C_2$, $C_2^8.(C_4\times S_4)$, $C_2^7.C_2^3:D_6.C_2$, $C_2^6.S_4.C_2^4$, $C_2^6.C_4^2.S_4$, $C_2^6.(D_4\times S_4).C_2$, $C_2^5.C_4^2.S_4.C_2$, $C_2^5.C_2^5.S_4$, $C_2^5.C_2^5.C_6.C_2^2$, $C_2^5.C_2^4.C_2^4.C_3$, $C_2^5.A_4.C_2\wr C_2^2$, $C_2^4.C_2^6.C_{12}.C_2$, $C_2^4.C_2^4.C_2^4:S_3$, $C_2^4.C_2^3.C_2^3:D_6.C_2$, $C_2^2.C_2^6.S_4.C_2^2$, $C_2^2.C_2^6.A_4.C_2^3$, $C_2^2.C_2^6.(C_4\times S_4)$

Order 23040: $(C_2^4\times A_4).S_5$ x 5, $C_2^4:A_4:S_5$ x 4, $S_4.C_2^4.A_5$ x 2, $C_4^2:A_4.S_5$ x 2, $C_2^6:C_3.S_5$, $C_2^5:S_6$, $C_2^5:S_6$

Order 20480: $C_2^6.C_2^4.D_{10}$ x 23, $C_2^6.C_2^4.C_{10}.C_2$ x 11, $C_2^2.C_2^4.C_2^4.D_{10}$ x 3, $C_2^6.C_2^4.F_5$ x 2, $C_2^2.C_2^4.C_2^4.F_5$ x 2, $C_2^8.C_2^4.C_5$, $C_2^5.(C_2^3\times D_5).C_2^3$, $C_2^5.C_2\wr F_5$, $C_2^5.C_2\wr F_5$, $C_2^{10}.F_5$

Order 19200: $(C_2^4\times A_5):F_5$ x 2, $(C_2^4\times D_5).S_5$

Order 18432: $C_2^6.A_4^2.C_2$ x 6, $C_2^8.A_4.S_3$ x 4, $C_2^6.A_4\wr C_2$ x 4, $C_2^4.C_2^6.C_3.S_3$ x 3, $C_4^4.(S_3\times A_4)$ x 2, $C_2^8.C_3:S_4$ x 2, $C_2^8.(S_3\times A_4)$ x 2, $C_2^8.\SOPlus(4,2)$ x 2, $C_2^8.\SOPlus(4,2)$ x 2, $C_4^2:A_4.C_2^4.C_6$, $C_2^6:C_3.C_2^4.C_6$, $C_2^6.(C_2^3\times C_6).C_6$, $C_2^4.C_2^4.(S_3\times A_4)$, $C_2^5.\POPlus(4,3)$, $C_2^5.A_4^2:C_4$, $C_2^5.S_4^2$, $C_2^8.(S_3\times A_4)$, $C_2^6.\PSOPlus(4,3)$, $C_2^8.(C_3\times S_4)$

Order 17408: $C_2^8.C_{17}:C_4$

Order 256: $C_2^8$

Order 1: $C_1$

Classes of subgroups up to automorphism

not computed

Normal subgroups (quotient in parentheses)

Order 501350400: $\ASigmaSp(4,4)$ ($C_1$)

Order 250675200: $C_2^8.\Sp(4,4)$ ($C_2$)

Order 256: $C_2^8$ ($\PSigmaSp(4,4)$)

Order 1: $C_1$ ($\ASigmaSp(4,4)$)

Normal subgroups up to automorphism (quotient in parentheses)

not computed

Series

Derived series	not computed
Chief series	not computed
Lower central series	not computed
Upper central series	not computed

Supergroups

This group is a maximal subgroup of 2 larger groups in the database.

This group is a maximal quotient of 0 larger groups in the database.

Character theory

Complex character table

See the $60 \times 60$ character table. Alternatively, you may search for characters of this group with desired properties.

Rational character table

See the $56 \times 56$ rational character table.