Finite Group Databasebeta

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C2×#13091426 #72243993

order2916
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×#13091426

Splittings

FittingC2×#10624869 ⋊ C2
Sylow#10624869 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C3×C9C3⋊(C3⋊D3)
commutator, cosocle, hypocenterC32⋊H(3,𝔽3)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624869C2
socleC2×C32C3×C3⋊(C3⋊D3)
prime radicalC2×#92338C3
LCSG ▷ C32⋊H(3,𝔽3)
UCSC1 ◁ C2×C3×C9

1371 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221829, C2×#72221830, C2×#72221851, …
maximal normal subgroup ofC2×#72221829, C2×#72221830, C2×#72221851, …
maximal quotient ofC2×#72221827

GAP

Past the SmallGroups library coverage — no SmallGroups id.