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SL(2,𝔽5)⋊C8 #11746444

order960
automorphism?
homologyAbelianization (H1) = C8 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productSL(2,𝔽5)⋊C8

Splittings

derivedSL(2,𝔽5) ⋊ C8

Subgroups

subgroupG/H
center, Frattini, Fitting, hypercenterC2×C4S5
commutator, hypocenterSL(2,𝔽5)C8
socleC22A5⋊C4
prime radicalC2×SL(2,𝔽5)C4
cosocleC4×SL(2,𝔽5)C2
LCSG ▷ SL(2,𝔽5)
UCSC1 ◁ C2×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Permutation generators:

(1,3,2,4)(5,7,6,8)(9,15,29,21,17,11,14,31,23,19,10,16,30,22,18,12,13,32,24,20)(25,27,26,28);(1,5,4,8,2,6,3,7)(9,22,11,24,10,21,12,23)(13,25,15,27,14,26,16,28)(17,29,19,31,18,30,20,32)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×SL(2,𝔽5)⋊C8, #14514977, #14514978, …
maximal normal subgroup ofC2×SL(2,𝔽5)⋊C8, #14514977, #14514978, …
maximal quotient ofSL(2,𝔽5)⋊C16, C2×SL(2,𝔽5)⋊C8

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 639);