Finite Group Databasebeta

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C22×#80002 #72246702

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productC22×#80002

Splittings

FittingC22×C3×#447 ⋊ C2
SylowC3 ⋊ C22×#3003

Subgroups

subgroupG/H
centerC24C2×D3×D4
commutator, cosocleC2×C3×C4C26
FrattiniC2×C4C25×D3
FittingC22×C3×#447C2
socleC24×C3C22×D4
hypercenterC22×#447D3
hypocenterC3C22×#3003
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#447

69980 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×D3×#3003
maximal normal subgroup ofC22×D3×#3003

GAP

Past the SmallGroups library coverage — no SmallGroups id.