Finite Group Databasebeta

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C2×#13091524 #72243946

order2916
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×#13091524

Splittings

FittingC2×#10624900 ⋊ C2
Sylow#10624900 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C3⋊AGL(1,ℤ/9))
commutator, cosocle, hypocenterC9×H(3,𝔽3)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624900C2
socleC2×C32C3×C3⋊(C3⋊D3)
prime radicalC2×C9⋊#272C3
LCSG ▷ C9×H(3,𝔽3)
UCSC1 ◁ C2×C3

889 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221823, C2×#72221864
maximal normal subgroup ofC2×#72221823, C2×#72221864
maximal quotient ofC2×#72221827

GAP

Past the SmallGroups library coverage — no SmallGroups id.