Finite Group Databasebeta

C2×C32×#940 #13179171

order1728
automorphism?
homologyAbelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3×C4

Aliases

direct productC2×C32×#940

Splittings

FittingC22×C33×D4 ⋊ C2
SylowC33 ⋊ C2×#127

Subgroups

subgroupG/H
centerC23×C32C22×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC22×C33×D4C2
socleC23×C33C23
hypercenterC22×C32×D4D3
hypocenterC3C2×C32×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C32 ◁ C22×C32×D4

3932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

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(1728, 45234);