Finite Group Databasebeta

#117×C3⋊D9 #13153872

order1728
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C3×C4

Aliases

direct product#117×C3⋊D9

Splittings

FittingC3×C9×#117 ⋊ C2
SylowC3×C9 ⋊ C2×#117

Subgroups

subgroupG/H
centerC2×C4C22×C3⋊D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C23×C3⋊D3
FittingC3×C9×#117C2
socleC22×C32C23×D3
prime radicalC23×C3⋊D9C22
cosocleC22×C3×C9C24
hypercenter#117C3⋊D9
hypocenterC3×C9C2×#117
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ #117

1650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19935);