Finite Group Databasebeta

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C3×C4×D4×A4 #11919672

order1152
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct productC3×C4×D4×A4
unambiguous semidirect product(C22×C4×D4)⋊C32
unambiguous semidirect product(C22×C3×C4×D4)⋊C3

Splittings

FittingC22×C3×C4×D4 ⋊ C3
SylowC22×C4×D4 ⋊ C32

Subgroups

subgroupG/H
centerC2×C3×C4C22×A4
commutatorC23C22×C32×C4
FrattiniC22C23×C3×A4
FittingC22×C3×C4×D4C3
socleC24×C3C23×C3
prime radicalC2×C3×D4×A4C2
cosocleC24C23×C32
hypercenterC3×C4×D4A4
hypocenterC22C32×C4×D4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

1344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153683);