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Cayley diagram

C3×#4208 #92390

order486
isoclinismisoclinic class of #272
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×#4208

Splittings

Fitting, SylowC3×#737 ⋊ C2

Subgroups

subgroupG/H
center, hypercenterC3×C9C3⋊D3
commutator, cosocle, hypocenterH(3,𝔽3)C2×C32
FrattiniC3C32×C3⋊D3
FittingC3×#737C2
socleC32C3×C3⋊D3
prime radicalC3×#272C3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C3×C9

204 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 81

A minimal faithful permutation representation — 3 generators on 30 points:

(4,5,8,7,10,16,14,20,26)(6,17,15,21,19,29,12,28,24,11,9,23,13,27,25,22,18,30);(1,2,3)(6,12,13)(9,18,19)(11,21,22)(15,24,25)(17,27,28)(23,29,30);(4,6,11)(5,9,17)(7,13,21)(8,15,23)(10,19,27)(12,22,14)(16,25,29)(18,28,20)(24,30,26)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

derived subgroup of(#4207⋊C2)⋊D3, #66419⋊D3
maximal subgroup ofC3×#66419, C3⋊#66419, D3×#4208, …
maximal normal subgroup ofC3×#66419, C3⋊#66419, D3×#4208, …
maximal quotient ofC3×#66410, C2×C3×#4208, C3×#92295, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 235);