Finite Group Databasebeta

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Cayley diagram

C2×D3×#168 #91285

order480
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×D3×#168

Splittings

derived, HallC3×C5 ⋊ C22×C8
SylowC5 ⋊ C2×D3×C8
SylowC3 ⋊ C22×#168

Subgroups

subgroupG/H
center, hypercenterC2×C4D3×D5
commutator, hypocenterC3×C5C22×C8
FrattiniC4C2×D3×D5
FittingC2×C3×C4×C5C22
socleC22×C3×C5C2×C4
prime radicalC22×C5×D3C4
cosocleC3×C4×C5C23
LCSG ▷ C3×C5
UCSC1 ◁ C2×C4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 240

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

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D3)⋊#674, C4×D3×#168, #11746977, …
maximal normal subgroup of(C2×D3)⋊#674, C4×D3×#168, #11746977, …
maximal quotient ofDic6×#168, #11746853, #11746857, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 361);