Finite Group Databasebeta

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C2×C3×#10619679 #72276199

order3888
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×#10619679

Splittings

FittingC23×C3×AΣL(1,𝔽27) ⋊ C2
SylowC3×AΣL(1,𝔽27) ⋊ C2×D4

Subgroups

subgroupG/H
centerC22×C3C2×#4183
commutator, cosocleC2×AΣL(1,𝔽27)C23×C3
FrattiniC2×C32C22×C3×C3⋊D3
FittingC23×C3×AΣL(1,𝔽27)C2
socleC22×C32C2×#272
hypercenterC23×C3#4183
hypocenterAΣL(1,𝔽27)C2×C3×D4
LCSG ▷ C2×AΣL(1,𝔽27) ▷ AΣL(1,𝔽27)
UCSC1 ◁ C22×C3 ◁ C23×C3

2110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

258 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.