Finite Group Databasebeta

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C2×#13091523 #72244032

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

Aliases

direct productC2×#13091523

Splittings

FittingC2×#10624900 ⋊ C2
Sylow#10624900 ⋊ C22

Subgroups

subgroupG/H
center, socleC2×C32C32×C3⋊D3
commutator, cosocleC3×H(3,𝔽3)C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624900C2
prime radicalC2×C3×#272C32
hypercenterC2×C9⋊C9C3⋊D3
hypocenterH(3,𝔽3)C22×3−1+2
LCSG ▷ C3×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C32 ◁ C2×C9⋊C9

737 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 486

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221830, C2×#72221864
maximal normal subgroup ofC2×#72221864
maximal quotient ofC2×#72221835

GAP

Past the SmallGroups library coverage — no SmallGroups id.