Finite Group Databasebeta

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C4×D3×C4⋊Dic3 #11800736

order1152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D3×C4⋊Dic3

Splittings

SylowC32 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C2×C4×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

1953 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 34747);