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Cayley diagram

A5⋊C8 #91141

order480
isoclinismisoclinic class of S5
automorphismAut(G) = C22×S5 (order 480) · Inn(G) = S5 · Out(G) = C22
homologyAbelianization (H1) = C8 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productA5⋊C8

Splittings

derivedA5 ⋊ C8

Subgroups

subgroupG/H
center, Frattini, Fitting, hypercenterC4S5
commutator, hypocenterA5C8
socle, prime radicalC2×A5C4
cosocleC4×A5C2
LCSG ▷ A5
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 40

A minimal faithful permutation representation — 2 generators on 13 points:

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

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×S5, #11751491, #11751496, …
maximal normal subgroup ofC8×S5, #11751491, #11751496, …
maximal quotient ofA5⋊C16, #11746443, SL(2,𝔽5)⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 217);