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Cayley diagram

C2×C5×SL(2,ℤ/4) #91946

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

Aliases

direct productC2×C5×SL(2,ℤ/4)
unambiguous semidirect product(C2×A4)⋊(C4×C5)

Splittings

derivedA4 ⋊ C2×C4×C5

Subgroups

subgroupG/H
center, hypercenterC22×C5S4
commutator, hypocenterA4C2×C4×C5
FrattiniC2C2×C5×S4
Fitting, socleC24×C5D3
prime radicalC22×C5×A4C2
cosocleC2×A4C22×C5
LCSG ▷ A4
UCSC1 ◁ C22×C5

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)(11,12,13,14,15);(1,2)(4,5,6)

Conjugacy classes & character table

100 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×C5×A4⋊C8, C5×#5409, C4×C5×SL(2,ℤ/4), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1022);