Finite Group Databasebeta

C32×#5111 #13162546

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

Aliases

direct productC32×#5111

Splittings

FittingC22×C33×C8 ⋊ C2
SylowC33 ⋊ #435

Subgroups

subgroupG/H
centerC2×C32×C4C22×D3
commutatorC22×C3C22×C32×C4
FrattiniC2×C4C22×C32×D3
FittingC22×C33×C8C2
socleC22×C33C22×C4
prime radicalC2×C32×#67C4
cosocleC2×C3×C4C23×C32
hypercenterC22×C32×C8D3
hypocenterC3C32×#435
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C32×C4 ◁ C22×C32×C8

1048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

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, 28609);