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Cayley diagram

C3×#4185 #92326

order486
isoclinismisoclinic class of #4185
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C3

Aliases

direct productC3×#4185

Splittings

Fitting, SylowC3×#732 ⋊ C2
derived#732 ⋊ C2×C3

Subgroups

subgroupG/H
center, hypercenterC3#4185
commutator, cosocle, hypocenter#732C2×C3
FrattiniC32C3×C3⋊D3
FittingC3×#732C2
socleC32#272
LCSG ▷ #732
UCSC1 ◁ C3

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 54

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

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

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#4178⋊C2, D3×#4185, #11757757, …
maximal normal subgroup ofC3×#4178⋊C2, D3×#4185, #11757757, …
maximal quotient ofC3×#66332, C2×C3×#4185, C3×#92198, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 171);