Finite Group Databasebeta

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C2×#10687757 #72253564

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#10687757

Splittings

FittingC2×C3×#1438 ⋊ C2
SylowC3 ⋊ C2×#8534

Subgroups

subgroupG/H
centerC23#4955
commutatorC24×C3C23×C4
FrattiniC25C23×D3
FittingC2×C3×#1438C2
socleC23×C3#379
prime radicalC2×#87239C2
cosocleC25×C3C24
hypercenterC2×#1438D3
hypocenterC3C2×#8534
LCSG ▷ C24×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C26 ◁ C2×#1438

9744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72231371, C2×D3×#8534, C2×#72231340, …
maximal normal subgroup ofC2×#72231371, C2×D3×#8534, C2×#72231340, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.