Finite Group Databasebeta

C32×C4×D24 #13162128

order1728
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC32×C4×D24

Splittings

FittingC33×C4×C8 ⋊ C2
SylowC33 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2×C32×C4D12
commutatorC3×C4C22×C32×C4
FrattiniC2×C4C22×C32×D3
FittingC33×C4×C8C2
socleC22×C33C2×D4
prime radicalC2×C32×D24C2
cosocleC2×C3×C4C23×C32
hypercenterC32×C4×C8D3
hypocenterC3C32×C4×D8
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C32×C4 ◁ C32×C42 ◁ C32×C4×C8

980 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 28191);