Finite Group Databasebeta

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Cayley diagram

C3×C4×C3⋊C8 #63588

order288
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4

Aliases

direct productC3×C4×C3⋊C8

Splittings

derivedC3 ⋊ C3×C4×C8
SylowC32 ⋊ C4×C8

Subgroups

subgroupG/H
center, hypercenterC3×C42D3
commutator, hypocenterC3C3×C4×C8
FrattiniC2×C4C2×C3×D3
FittingC32×C42C2
socle, prime radicalC22×C32C2×C4
cosocleC2×C3×C4C22×C3
LCSG ▷ C3
UCSC1 ◁ C3×C42

103 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 96

A minimal faithful permutation representation — 2 generators on 18 points:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊C82, #10589078, #10589079, …
maximal normal subgroup ofC3⋊C82, #10589078, #10589079, …
maximal quotient ofC3×C8×C3⋊C8, C3×#4455, C3×C4×C3⋊C16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 236);