Finite Group Databasebeta

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C2×#10624887⋊C2 #72244086

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

Aliases

direct productC2×#10624887⋊C2

Splittings

FittingC2×#10624887 ⋊ C2
Sylow#10624887 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C3#4207⋊C3
commutator, cosocleC32×C9C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624887C2
socleC2×C32C32×C3⋊D3
prime radicalC2×C3×#4207C3
hypocenterC3×C9C22×3−1+2
LCSG ▷ C32×C9 ▷ C3×C9
UCSC1 ◁ C2×C3

585 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×#72221844, C2×#72221842, C2×#72221843, …
maximal normal subgroup ofC2×#72221845

GAP

Past the SmallGroups library coverage — no SmallGroups id.