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Cayley diagram

A4×Dic10 #91959

order480
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productA4×Dic10
unambiguous semidirect productC5⋊(Q8×A4)
unambiguous semidirect product(C22×Dic10)⋊C3

Splittings

HallC22×Dic10 ⋊ C3
SylowC5 ⋊ Q8×A4

Subgroups

subgroupG/H
center, FrattiniC2C2×D5×A4
commutator, socle, cosocleC23×C5C22×C3
FittingC22×C4×C5C2×C3
prime radicalC2×C5×A4C22
hypercenterC4D5×A4
hypocenterC22×C5C3×Q8
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C2 ◁ C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 17 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11751583, #11751584, #11751585, …
maximal normal subgroup of#11751583, #11751584, #11751585, …
maximal quotient ofSL(2,𝔽3)×Dic10, #65903⋊C3, #65904⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1035);