Finite Group Databasebeta

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C2×#10826482 #72258800

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

Aliases

direct productC2×#10826482

Splittings

FittingC2×C3×#1795 ⋊ C2
SylowC3 ⋊ C2×#23872

Subgroups

subgroupG/H
centerC22#73852
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC2×C3×#1795C2
socleC22×C3#2403
hypercenterC2×#1795D3
hypocenterC3C2×#23872
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#1795

12892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.