Finite Group Databasebeta

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C2×#13091651 #72244447

order2916
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C33

Aliases

direct productC2×#13091651

Splittings

FittingC2×#10624931 ⋊ C2
Sylow#10624931 ⋊ C22

Subgroups

subgroupG/H
center, socle, hypercenterC2×C3C3⋊(C3⋊((C3⋊D3)⋊C3))
commutator, cosocle, hypocenterH(5,𝔽3)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624931C2
prime radicalC2×#92404C3
LCSG ▷ H(5,𝔽3)
UCSC1 ◁ C2×C3

1261 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221886, C2×#72221888, C2×#72221891
maximal normal subgroup ofC2×#72221886, C2×#72221888, C2×#72221891

GAP

Past the SmallGroups library coverage — no SmallGroups id.