Finite Group Databasebeta

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C2×C3⋊#92281 #72253994

order2916
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×C3⋊#92281

Splittings

FittingC2×C3×#6909 ⋊ C2
SylowC3×#6909 ⋊ C22

Subgroups

subgroupG/H
centerC2×C3C3×C3⋊((C3⋊D3)⋊C3)
commutator, cosocle, hypocenterC3×H(3,𝔽3)C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×C3×#6909C2
socleC2×C32C3×(C3⋊D3)⋊C3
hypercenterC2×C32C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3 ◁ C2×C32

1070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221874, C2×#72221877, C2×#72221878, …
maximal normal subgroup ofC2×#72221880, C2×#72221881

GAP

Past the SmallGroups library coverage — no SmallGroups id.