Finite Group Databasebeta

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Cayley diagram

C2×C4⋊(C3⋊D9) #88735

order432
isoclinismisoclinic class of #6226
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C4⋊(C3⋊D9)

Splittings

FittingC2×C3×C4×C9 ⋊ C2
SylowC3×C9 ⋊ C2×D4

Subgroups

subgroupG/H
centerC22C2×C3⋊D9
commutator, cosocleC2×C3×C9C23
FrattiniC2×C3C22×C3⋊D3
FittingC2×C3×C4×C9C2
socleC22×C32C2×D3
hypercenterC2×C4C3⋊D9
hypocenterC3×C9C2×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×C4

270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 216

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

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

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11720267, #11720284, #11720288, …
maximal normal subgroup of#11720267, #11720284, #11720288, …
maximal quotient of#11721706, C4×C4⋊(C3⋊D9), #11721711, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 382);