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Cayley diagram

C2×A4⋊Dic5 #91957

order480
isoclinismisoclinic class of C5⋊S4
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×A4⋊Dic5
unambiguous semidirect product(C2×A4)⋊Dic5

Splittings

derivedC5×A4 ⋊ C2×C4
SylowC5 ⋊ C2×SL(2,ℤ/4)

Subgroups

subgroupG/H
center, hypercenterC22C5⋊S4
commutator, hypocenterC5×A4C2×C4
FrattiniC2C2×C5⋊S4
Fitting, socleC24×C5D3
prime radicalC22×C5×A4C2
cosocleC2×C5×A4C22
LCSG ▷ C5×A4
UCSC1 ◁ C22

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 15 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×SL(2,ℤ/4), #11751634, SL(2,ℤ/4)⋊Dic5, …
maximal normal subgroup ofDic5×SL(2,ℤ/4), #11751634, SL(2,ℤ/4)⋊Dic5, …
maximal quotient ofC2×A4⋊#168, #11752128, C4×A4⋊Dic5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1033);