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A5⋊C32 #14514719

order1920
isoclinismisoclinic class of S5
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productA5⋊C32

Splittings

derivedA5 ⋊ C32

Subgroups

subgroupG/H
center, Frattini, Fitting, hypercenterC16S5
commutator, hypocenterA5C32
socle, prime radicalC2×A5C16
cosocleC16×A5C2
LCSG ▷ A5
UCSC1 ◁ C16

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Permutation generators:

(1,3,5,2)(6,33,19,23,12,34,14,29,9,31,20,24,10,37,17,27,7,32,18,22,13,35,15,28,8,30,21,25,11,36,16,26);(1,4,5)(6,16,11,21,8,15,13,18,7,17,10,20,9,14,12,19)(22,32,27,37,24,31,29,34,23,33,26,36,25,30,28,35)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240417);