Finite Group Databasebeta

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C2×#10826764 #72248571

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C212

Aliases

direct productC2×#10826764

Splittings

FittingC23×C3×#120 ⋊ C2
SylowC3 ⋊ C2×#23900

Subgroups

subgroupG/H
centerC23C2×#937
commutator, cosocleC24×C3C25
FrattiniC24C24×D3
FittingC23×C3×#120C2
socleC23×C3C2×#120
hypercenterC23×#120D3
hypocenterC3C2×#23900
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C26 ◁ C23×#120

29984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#23900, C2×#72231325, C2×#72231340, …
maximal normal subgroup ofC2×D3×#23900, C2×#72231325, C2×#72231340, …
maximal quotient ofC2×#72231658

GAP

Past the SmallGroups library coverage — no SmallGroups id.