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C4⋊#6728 #11751503

order960
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC4⋊#6728

Subgroups

subgroupG/H
center, Frattini, socleC22C2×S5
commutator, prime radical, cosocleC2×SL(2,𝔽5)C22
Fitting, hypercenterC2×C4S5
hypocenterSL(2,𝔽5)D4
LCSG ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5)
UCSC1 ◁ C22 ◁ C2×C4

115 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Permutation generators:

(1,4,2,3)(5,44,6,43)(7,11,8,12)(9,29,10,30)(13,20,14,19)(15,24,16,23)(17,22,18,21)(25,40,26,39)(27,36,28,35)(31,50,32,49)(33,37,34,38)(41,52,42,51)(45,47,46,48);(1,4)(2,3)(5,28,12,42,6,27,11,41)(7,46,25,35,8,45,26,36)(9,37,24,13,10,38,23,14)(15,52,18,48,16,51,17,47)(19,39,31,43,20,40,32,44)(21,49,30,34,22,50,29,33)

Conjugacy classes & character table

33 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14515008, #14515009, #14515011, …
maximal normal subgroup of#14515008, #14515009, #14515011, …
maximal quotient of#14514938, C4⋊#91143, #14515011, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 5698);