Finite Group Databasebeta

C2×C3×C4×#208 #11857147

order1152
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C3×C4×#208

Splittings

SylowC32 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C3×C42C2×D3
commutatorC2×C3C22×C3×C42
FrattiniC2×C4C23×C3×D3
FittingC22×C32×C42C2
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC2×C3×C4C24×C3
hypercenterC22×C3×C42D3
hypocenterC3C2×C3×C4×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C42 ◁ C22×C3×C42

1561 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, 91158);