Finite Group Databasebeta

C2×C3×D3×#95 #11800652

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C28

Aliases

direct productC2×C3×D3×#95

Splittings

FittingC2×C32×#95 ⋊ C2
SylowC32 ⋊ C22×#95

Subgroups

subgroupG/H
centerC24×C3C22×D3
commutatorC2×C3C22×C3×C42
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socleC24×C32C23
prime radicalC24×C3×D3C22
cosocleC23×C3C24×C3
hypercenterC2×C3×#95D3
hypocenterC3C22×C3×#95
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

3925 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

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, 34663);