Finite Group Databasebeta

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C2×#4207⋊C9 #72243924

order2916
automorphism?
homologyAbelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×#4207⋊C9

Splittings

FittingC2×#10624864 ⋊ C2
derivedC3×C9 ⋊ C22×C3×C9
Sylow#10624864 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C3#4207⋊C3
commutator, hypocenterC3×C9C22×C3×C9
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624864C2
socleC2×C32C32×C3⋊D3
prime radicalC2×C3×#4207C3
cosocleC32×C9C22×C32
LCSG ▷ C3×C9
UCSC1 ◁ C2×C3

755 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#72221820, C2×#72221823, C2×#72221824, …
maximal normal subgroup ofC2×#72221845, C2×#72221858

GAP

Past the SmallGroups library coverage — no SmallGroups id.