Finite Group Databasebeta

← Prev (#10953374) Next (#10953376) →

C42×D3×D4 #10953375

order768
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC42×D3×D4

Splittings

FittingC3×C42×D4 ⋊ C2
SylowC3 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC2×C42C22×D3
commutatorC2×C3C23×C42
FrattiniC23C24×D3
FittingC3×C42×D4C2
socle, cosocleC23×C3C25
prime radicalC22×D3×D4C22
hypercenterC42×D4D3
hypocenterC3C2×C42×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C42 ◁ C42×D4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#21503, D3×#36260, D3×#34310, …
maximal normal subgroup ofD3×#21503, D3×#36260, D3×#34310, …
maximal quotient ofD3×#20512, D3×D4×#95, C4×D3×#442

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 327756);