Finite Group Databasebeta

C2×C3×C4×#235 #11899953

order1152
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C3×C4×#235

Splittings

FittingC22×C32×C42 ⋊ C2
SylowC32 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC2×C3×C42C2×D3
commutatorC2×C3C24×C3×C4
FrattiniC22C24×C3×D3
FittingC22×C32×C42C2
socleC23×C32C24
prime radicalC22×C3×#235C2
cosocleC22×C3C25×C3
hypercenterC22×C3×C42D3
hypocenterC3C2×C3×C4×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C42 ◁ C22×C3×C42

3705 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 133964);