Finite Group Databasebeta

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#11757162

order960
isoclinismisoclinic class of #11757162
automorphismAut(G) = #72240863 (order 23040) · Inn(G) = G · Out(G) = S4
homologyAbelianization (H1) = C1 · Schur multiplier (H2) = C2×C42

Aliases

No aliases for this group.

Splittings

Fitting, socleC24 ⋊ A5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, hypocenterGC1
Fitting, socle, cosocleC24A5
LCSG
UCSC1

77 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 16

A minimal faithful permutation representation — 2 generators on 16 points:

(1,4,2)(3,10,6)(5,13,9)(8,14,12)(11,16,15);(1,12,7,3)(2,8,4,5)(6,10,13,11)(9,16,15,14)

Conjugacy classes & character table

C1C2C3C4C5C6C7C8C9
size11560606060192192320
order122444553
χ1111111111
χ233-1-1-1-11−521+520
χ333-1-1-1-11+521−520
χ4440000-1-11
χ555111100-1
χ615-13-1-1-1000
χ715-1-13-1-1000
χ815-1-1-13-1000
χ915-1-1-1-13000

Relationships

derived subgroup ofAΣL(2,𝔽4), C2×#11757162, #14515297, …
maximal subgroup ofAΣL(2,𝔽4), C2×#11757162, #14515297, …
maximal normal subgroup ofAΣL(2,𝔽4), C2×#11757162, #14515297, …
maximal quotient ofC2×#11757162, #14515300, #14515301, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11357);