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C2×C3×A6 #72228167

order2160
isoclinismisoclinic class of A6
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×A6

Subgroups

subgroupG/H
center, Fitting, hypercenterC2×C3A6
commutator, hypocenterA6C2×C3
FrattiniC1G
LCSG ▷ A6
UCSC1 ◁ C2×C3

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 11
transitive degreeμt(G) = 36

A minimal faithful permutation representation — 2 generators on 11 points:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

socle ofDic3×A6
maximal subgroup ofSL(2,𝔽3)×A6, Dic3×A6
maximal normal subgroup ofDic3×A6

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((6,9,11), (1,2)(3,4,5)(6,7,8,10,9));