Finite Group Databasebeta

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C2×#10826739 #72253993

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

Aliases

direct productC2×#10826739

Splittings

FittingC2×C3×#1781 ⋊ C2
SylowC3 ⋊ C2×#23895

Subgroups

subgroupG/H
centerC22#73852
commutator, cosocleC24×C3C25
FrattiniC24C24×D3
FittingC2×C3×#1781C2
socleC22×C3#2403
hypercenterC2×#1781D3
hypocenterC3C2×#23895
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ C2×#1781

14444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72231723, C2×D3×#23895, C2×#72231726, …
maximal normal subgroup ofC2×#72231723, C2×D3×#23895, C2×#72231726, …
maximal quotient ofC2×#72231824

GAP

Past the SmallGroups library coverage — no SmallGroups id.