Finite Group Databasebeta

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Cayley diagram

C4×C3⋊Dic9 #88533

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

Aliases

direct productC4×C3⋊Dic9

Splittings

derived, SylowC3×C9 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC2×C4C3⋊D9
commutator, hypocenterC3×C9C42
FrattiniC22×C3C2×C3⋊D3
FittingC2×C3×C4×C9C2
socle, prime radicalC22×C32C2×D3
cosocleC22×C3×C9C22
LCSG ▷ C3×C9
UCSC1 ◁ C2×C4

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 432

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11720271, #11720273, #11720275, …
maximal normal subgroup of#11720271, #11720273, #11720275, …
maximal quotient ofC4×C3⋊(C9⋊C8), #11720516, C8×C3⋊Dic9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 180);