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A5⋊C16 #11746442

order960
isoclinismisoclinic class of S5
automorphism?
homologyAbelianization (H1) = C16 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productA5⋊C16

Splittings

derivedA5 ⋊ C16

Subgroups

subgroupG/H
center, Frattini, Fitting, hypercenterC8S5
commutator, hypocenterA5C16
socle, prime radicalC2×A5C8
cosocleC8×A5C2
LCSG ▷ A5
UCSC1 ◁ C8

61 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Permutation generators:

(1,3,5)(6,13,9,11,7,12,8,10)(14,21,17,19,15,20,16,18);(1,5,4)(2,3)(6,17,11,20,8,14,13,19,7,16,10,21,9,15,12,18)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×A5⋊C16, C16×S5, #14514768, …
maximal normal subgroup ofC2×A5⋊C16, C16×S5, #14514768, …
maximal quotient ofA5⋊C32, C2×A5⋊C16, SL(2,𝔽5)⋊C16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 637);