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Cayley diagram

C2×A4×Dic5 #91968

order480
isoclinismisoclinic class of D5×A4
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×A4×Dic5
unambiguous semidirect product(C23×Dic5)⋊C3

Splittings

derivedC22×C5 ⋊ C2×C3×C4
HallC23×Dic5 ⋊ C3
SylowC5 ⋊ C2×C4×A4

Subgroups

subgroupG/H
center, hypercenterC22D5×A4
commutator, hypocenterC22×C5C2×C3×C4
FrattiniC2C2×D5×A4
Fitting, socleC24×C5C2×C3
prime radicalC22×C5×A4C2
cosocleC23×C5C22×C3
LCSG ▷ C22×C5
UCSC1 ◁ C22

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:

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

Conjugacy classes & character table

64 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, A4×#681, C4×A4×Dic5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1044);