Finite Group Databasebeta

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Cayley diagram

C2×C4×C3⋊D9 #88734

order432
isoclinismisoclinic class of C3⋊D9
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C4×C3⋊D9

Splittings

FittingC2×C3×C4×C9 ⋊ C2
derived, SylowC3×C9 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4C3⋊D9
commutator, hypocenterC3×C9C22×C4
FrattiniC2×C3C22×C3⋊D3
FittingC2×C3×C4×C9C2
socleC22×C32C2×D3
prime radicalC22×C3⋊D9C2
cosocleC2×C3×C9C23
LCSG ▷ C3×C9
UCSC1 ◁ 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:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11720282, #11720542, C2×(C3⋊D9)⋊C8, …
maximal normal subgroup of#11720282, #11720542, C2×(C3⋊D9)⋊C8, …
maximal quotient ofC4×#6226, C42×C3⋊D9, #11721709, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 381);