Finite Group Databasebeta

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C2×#10624904⋊C2 #72243947

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

Aliases

direct productC2×#10624904⋊C2

Splittings

FittingC2×#10624904 ⋊ C2
Sylow#10624904 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊#4207
commutator, cosocle, hypocenterC9×H(3,𝔽3)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624904C2
socleC2×C32C3×C3⋊(C3⋊D3)
prime radicalC2×C9⋊#272C3
LCSG ▷ C9×H(3,𝔽3)
UCSC1 ◁ C2×C3

691 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
maximal normal subgroup ofC2×#72221823

GAP

Past the SmallGroups library coverage — no SmallGroups id.