Finite Group Databasebeta

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C2×#10826820 #72258690

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC2×#10826820

Splittings

FittingC2×C3×#3003 ⋊ C2
SylowC3 ⋊ C2×#23906

Subgroups

subgroupG/H
centerC23C2×#937
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC2×C3×#3003C2
socleC23×C3C2×#120
hypercenterC2×#3003D3
hypocenterC3C2×#23906
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#3003

18988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#23906
maximal normal subgroup ofC2×D3×#23906

GAP

Past the SmallGroups library coverage — no SmallGroups id.