Finite Group Databasebeta

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C4×D3×D4×C3⋊D3 #72252916

order3456
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C3

Aliases

direct productC4×D3×D4×C3⋊D3

Splittings

FittingC33×C4×D4 ⋊ C22
SylowC33 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC2×C4C22×D3×C3⋊D3
commutatorC2×C33C24×C4
FrattiniC22C23×D3×C3⋊D3
FittingC33×C4×D4C22
socle, cosocleC22×C33C25
prime radicalC2×D3×D4×C3⋊D3C2
hypercenterC4×D4D3×C3⋊D3
hypocenterC33C22×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C4×D4

16872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C3⋊D3×#442
maximal normal subgroup ofD3×C3⋊D3×#442
maximal quotient ofD3×C3⋊D3×#442

GAP

Past the SmallGroups library coverage — no SmallGroups id.