Finite Group Databasebeta

← Prev (#72254018) Next (#72254020) →

C2×C3⋊(#6913⋊C2) #72254019

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

Aliases

direct productC2×C3⋊(#6913⋊C2)

Splittings

FittingC2×C3×#6913 ⋊ C2
SylowC3×#6913 ⋊ C22

Subgroups

subgroupG/H
centerC2×C3C3×C3⋊((C3⋊D3)⋊C3)
commutator, cosocle, hypocenterC3×H(3,𝔽3)C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×C3×#6913C2
socleC2×C32C3×(C3⋊D3)⋊C3
hypercenterC2×C9C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3 ◁ C2×C9

848 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×#72221891, C2×#72221894
maximal normal subgroup ofC2×#72221894

GAP

Past the SmallGroups library coverage — no SmallGroups id.