Finite Group Databasebeta

C3×(Q8⋊C9)⋊C9 #14517224

order1944
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC3×(Q8⋊C9)⋊C9

Splittings

SylowQ8 ⋊ C3×C9⋊C9

Subgroups

subgroupG/H
center, socle, prime radicalC2×C33C3×A4
commutatorC3×Q8C32×C9
FrattiniC2×C32C32×A4
FittingC32×Q8×C9C3
cosocleC32×Q8C33
hypercenterC2×C32×C9A4
hypocenterQ8C3×C9⋊C9
LCSG ▷ C3×Q8 ▷ Q8
UCSC1 ◁ C2×C33 ◁ C2×C32×C9

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1944

Conjugacy classes & character table

279 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1618);