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Cayley diagram

C3×C4×Dic9 #88481

order432
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C4

Aliases

direct productC3×C4×Dic9

Splittings

derivedC9 ⋊ C3×C42
SylowC3×C9 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4D9
commutator, hypocenterC9C3×C42
FrattiniC22×C3C2×C3×D3
FittingC2×C3×C4×C9C2
socle, prime radicalC22×C32C2×D3
cosocleC22×C9C22×C3
LCSG ▷ C9
UCSC1 ◁ C2×C3×C4

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 144

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3)(5,7)(6,10)(8,9)(11,12)(17,20,19,18);(4,12,7,10,9,8,6,5,11)(13,16,15,14)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊C8×Dic9, Dic9⋊(C3⋊C8), #11720274, …
maximal normal subgroup ofC3⋊C8×Dic9, Dic9⋊(C3⋊C8), #11720274, …
maximal quotient ofC3×C4×C9⋊C8, C3×#63362, C3×C8×Dic9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 128);