Finite Group Databasebeta

C3×C4×D3×C22⋊C4 #11800682

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC3×C4×D3×C22⋊C4

Splittings

FittingC32×C4×C22⋊C4 ⋊ C2
SylowC32 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC2×C3C22×C3×C42
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
prime radicalC24×C3×D3C22
cosocleC23×C3C24×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C2×C3×C4×C22⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

2849 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 34693);