Finite Group Databasebeta

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C2×C3×C4×#4183 #72276089

order3888
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×C4×#4183

Splittings

FittingC2×C3×C4×AΣL(1,𝔽27) ⋊ C2
derivedAΣL(1,𝔽27) ⋊ C22×C3×C4
SylowC3×AΣL(1,𝔽27) ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4#4183
commutator, hypocenterAΣL(1,𝔽27)C22×C3×C4
FrattiniC2×C32C22×C3×C3⋊D3
FittingC2×C3×C4×AΣL(1,𝔽27)C2
socleC22×C32C2×#272
prime radicalC22×C3×#4183C2
cosocleC2×AΣL(1,𝔽27)C23×C3
LCSG ▷ AΣL(1,𝔽27)
UCSC1 ◁ C2×C3×C4

1838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.