Finite Group Databasebeta

C32×#4745 #13162181

order1728
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC32×#4745

Splittings

FittingC33×#100 ⋊ C2
SylowC33 ⋊ #413

Subgroups

subgroupG/H
centerC2×C32D3×C22⋊C4
commutatorC22×C3C22×C32×C4
FrattiniC2×C4C22×C32×D3
FittingC33×#100C2
socleC2×C33C2×C22⋊C4
prime radicalC2×C32×#237C2
cosocleC2×C3×C4C23×C32
hypercenterC32×#100D3
hypocenterC3C32×#413
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C32 ◁ C2×C32×C4 ◁ C32×#100

1084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 28244);