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Cayley diagram

C3×C42×D3 #63994

order288
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×C42×D3

Splittings

FittingC32×C42 ⋊ C2
derivedC3 ⋊ C2×C3×C42
SylowC32 ⋊ C2×C42

Subgroups

subgroupG/H
center, hypercenterC3×C42D3
commutator, hypocenterC3C2×C3×C42
FrattiniC22C22×C3×D3
FittingC32×C42C2
socleC22×C32C23
prime radicalC22×C3×D3C22
cosocleC22×C3C23×C3
LCSG ▷ C3
UCSC1 ◁ C3×C42

231 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 96

A minimal faithful permutation representation — 3 generators on 14 points:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10590248, #10590261, #10590262, …
maximal normal subgroup of#10590248, #10590261, #10590262, …
maximal quotient ofC3×#4648, C3×#4649, C3×D3×#95, …
automorphism group ofC22×C5×C13, C5×D3×C13
outer automorphism group ofC22×C5×C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 642);