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D3×D4×S4 #11923548

order1152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD3×D4×S4

Splittings

FittingC22×C3×D4 ⋊ C2×D3

Subgroups

subgroupG/H
center, FrattiniC2C22×D3×S4
commutator, cosocleC2×C3×A4C24
FittingC22×C3×D4C2×D3
socleC23×C3C23×D3
hypercenterD4D3×S4
hypocenterC3×A4C22×D4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ D4

2644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×S42, #72222977, D4×((C3⋊S4)⋊C3)⋊C2, …
maximal normal subgroup ofC3×D3×D4×S4, C2×D3×D4×S4, D3×#87477, …
maximal quotient of#72222977, D4×((C3⋊S4)⋊C3)⋊C2, S4×#3811, …
automorphism group of#1009, #1010, A4×Dic6, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 157559);