Finite Group Databasebeta

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C4×D3×#392 #72271073

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productC4×D3×#392

Splittings

FittingC3×C4×#392 ⋊ C2
SylowC3 ⋊ C2×C4×#392

Subgroups

subgroupG/H
centerC23×C4C23×D3
commutatorC23×C3C24×C4
FrattiniC24C24×D3
FittingC3×C4×#392C2
socle, cosocleC24×C3C25
prime radicalC2×D3×#392C2
hypercenterC4×#392D3
hypocenterC3C2×C4×#392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C4×#392

26772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×#609884, D3×#4306523, D3×#772785
maximal normal subgroup ofD3×#609884, D3×#4306523, D3×#772785

GAP

Past the SmallGroups library coverage — no SmallGroups id.