Finite Group Databasebeta

C32×#5827 #13179199

order1728
automorphism?
homologyAbelianization (H1) = C23×C32×C4 · Schur multiplier (H2) = C25×C3

Aliases

direct productC32×#5827

Splittings

SylowC33 ⋊ #520

Subgroups

subgroupG/H
centerC22×C32C23×D3
commutatorC2×C3C23×C32×C4
FrattiniC22C23×C32×D3
Fitting, prime radicalC2×C33×#41C2
socleC22×C33C24
cosocleC22×C3C24×C32
hypercenterC2×C32×#41D3
hypocenterC3C32×#520
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C2×C32×#41

2420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 45262);