Finite Group Databasebeta

C32×#5964 #13181723

order1728
automorphism?
homologyAbelianization (H1) = C25×C32 · Schur multiplier (H2) = C29×C3

Aliases

direct productC32×#5964

Splittings

FittingC2×C33×#41 ⋊ C2
SylowC33 ⋊ #585

Subgroups

subgroupG/H
centerC32×C4C23×D3
commutator, cosocleC2×C3C25×C32
FrattiniC2C24×C32×D3
FittingC2×C33×#41C2
socleC2×C33C25
hypercenterC2×C32×#41D3
hypocenterC3C32×#585
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C32×C4 ◁ C2×C32×#41

5516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

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, 47786);