Finite Group Databasebeta

C2×C3×C4×D24 #11859823

order1152
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×C4×D24

Splittings

FittingC2×C32×C4×C8 ⋊ C2
SylowC32 ⋊ C2×C4×D8

Subgroups

subgroupG/H
centerC22×C3×C4D12
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×C8C2
socleC23×C32C2×D4
prime radicalC22×C3×D24C2
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×C4×C8D3
hypocenterC3C2×C3×C4×D8
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×C8

1313 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, 93834);