Finite Group Databasebeta

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Cayley diagram

C2×C4×Dic15 #91811

order480
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×Dic15

Splittings

derived, HallC3×C5 ⋊ C2×C42
SylowC5 ⋊ C2×C4×Dic3
SylowC3 ⋊ C2×C4×Dic5

Subgroups

subgroupG/H
center, hypercenterC22×C4D15
commutator, hypocenterC3×C5C2×C42
FrattiniC22C22×D15
FittingC22×C3×C4×C5C2
socle, prime radicalC23×C3×C5C22
cosocleC22×C3×C5C23
LCSG ▷ C3×C5
UCSC1 ◁ C22×C4

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 18 points:

(1,2)(4,5)(6,7,8,9)(15,16)(17,18);(3,4,5)(10,11,12,13)(14,15,17,18,16);(1,2)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745968, #11745973, #11745975, …
maximal normal subgroup of#11745968, #11745973, #11745975, …
maximal quotient ofC2×C4×C3⋊#168, C2×#91087, C4×#6710, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 887);