Finite Group Databasebeta

C2×C9×#942 #13153641

order1728
automorphism?
homologyAbelianization (H1) = C24×C9 · Schur multiplier (H2) = C25

Aliases

direct productC2×C9×#942

Splittings

FittingC22×C3×Q8×C9 ⋊ C2
SylowC3×C9 ⋊ C2×#137

Subgroups

subgroupG/H
centerC22×C9C2×#67
commutatorC3×C4C24×C9
FrattiniC3×C4C23×C3×D3
FittingC22×C3×Q8×C9C2
socleC22×C32C2×C3×D4
prime radicalC2×C3×#235C2×C3
cosocleC32×C4C24×C3
hypercenterC22×Q8×C9D3
hypocenterC3C2×C9×#137
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C9 ◁ C22×C4×C9 ◁ C22×Q8×C9

930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19704);