Finite Group Databasebeta

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C2×#10949243 #72248588

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#10949243

Splittings

FittingC2×C3×#2199 ⋊ C2
SylowC3 ⋊ C2×#33551

Subgroups

subgroupG/H
centerC22D3×B(4,𝔽2)
commutator, cosocleC2×C3×D4C25
FrattiniC2×D4C24×D3
FittingC2×C3×#2199C2
socleC22×C3C2×B(4,𝔽2)
hypercenterC2×#2199D3
hypocenterC3C2×#33551
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#2199

9028 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#33551
maximal normal subgroup ofC2×D3×#33551
maximal quotient of#72270770

GAP

Past the SmallGroups library coverage — no SmallGroups id.