Finite Group Databasebeta

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C2×#10687790 #72253655

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#10687790

Splittings

SylowC3 ⋊ C2×#8541

Subgroups

subgroupG/H
centerC23#5247
commutatorC24×C3C23×C4
FrattiniC25C23×D3
Fitting, prime radicalC23×C3×#120C2
socleC23×C3#379
cosocleC25×C3C24
hypercenterC23×#120D3
hypocenterC3C2×#8541
LCSG ▷ C24×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C26 ◁ C23×#120

23164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#8541, C2×#72230825, C2×#72231340, …
maximal normal subgroup ofC2×D3×#8541, C2×#72230825, C2×#72231340, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.