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Cayley diagram

C3×#4176 #92273

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

Aliases

direct productC3×#4176

Splittings

Fitting, SylowC3×#731 ⋊ C2

Subgroups

subgroupG/H
center, socle, hypercenterC32(C3⋊D3)⋊C3
commutator, cosocle, hypocenterH(3,𝔽3)C2×C32
FrattiniC32C32×D3
FittingC3×#731C2
prime radicalC3×#272C3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C32

84 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:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#4176⋊C2, D3×#4176, #11757738, …
maximal normal subgroup ofC3×#4176⋊C2, D3×#4176, #11757738, …
maximal quotient ofC3×#66323, C2×C3×#4176, C3×#92162, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 118);