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Cayley diagram

C3×#4178 #92276

order486
isoclinismisoclinic class of #4174
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×#4178

Splittings

Fitting, SylowC3×#732 ⋊ C2

Subgroups

subgroupG/H
center, socle, hypercenterC32(C3⋊D3)⋊C3
commutator, cosocle, hypocenterH(3,𝔽3)C2×C32
FrattiniC32C32×D3
FittingC3×#732C2
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#4178⋊C2, D3×#4178, #11757741, …
maximal normal subgroup ofC3×#4178⋊C2, D3×#4178, #11757741, …
maximal quotient ofC3×#66325, C2×C3×#4178, C3×#92160, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 121);