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Cayley diagram

C8×A5 #91144

order480
isoclinismisoclinic class of A5
automorphismAut(G) = C22×S5 (order 480) · Inn(G) = A5 · Out(G) = C23
homologyAbelianization (H1) = C8 · Schur multiplier (H2) = C2

Aliases

direct productC8×A5

Subgroups

subgroupG/H
center, Fitting, hypercenterC8A5
commutator, hypocenterA5C8
Frattini, cosocleC4C2×A5
socle, prime radicalC2×A5C4
LCSG ▷ A5
UCSC1 ◁ C8

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:

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

derived subgroup of#14514771, #14514772, D16×A5, …
maximal subgroup ofA5⋊C16, C16×A5, C8×S5, …
maximal normal subgroup ofA5⋊C16, C16×A5, C8×S5, …
maximal quotient ofC16×A5, #11746446, C8×SL(2,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 220);