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Cayley diagram

C2×C4×C5×A4 #92050

order480
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×C4×C5×A4
unambiguous semidirect product(C23×C4)⋊(C3×C5)
unambiguous semidirect product(C23×C4×C5)⋊C3

Splittings

Fitting, HallC23×C4×C5 ⋊ C3
derivedC22 ⋊ C2×C3×C4×C5
SylowC23×C4 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5A4
commutator, hypocenterC22C2×C3×C4×C5
FrattiniC2C22×C5×A4
FittingC23×C4×C5C3
socleC24×C5C2×C3
prime radicalC22×C5×A4C2
cosocleC23C22×C3×C5
LCSG ▷ C22
UCSC1 ◁ C2×C4×C5

132 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:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×A4⋊C8, C5×#5409, C4×C5×SL(2,ℤ/4), …
maximal normal subgroup ofC2×C5×A4⋊C8, C5×#5409, C4×C5×SL(2,ℤ/4), …
maximal quotient ofC42×C5×A4, C5×A4×C22⋊C4, C5×A4×C4⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1126);