Finite Group Databasebeta

C3×(C79⋊C9)⋊C9 #34063231

order19197
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC3×(C79⋊C9)⋊C9

Splittings

SylowC79 ⋊ C3×C9⋊C9

Subgroups

subgroupG/H
centerC33C3×C79⋊C3
commutatorC3×C79C32×C9
FrattiniC32C32×C79⋊C3
FittingC32×C9×C79C3
socle, prime radicalC33×C79C32
cosocleC32×C79C33
hypercenterC32×C9C79⋊C3
hypocenterC79C3×C9⋊C9
LCSG ▷ C3×C79 ▷ C79
UCSC1 ◁ C33 ◁ C32×C9

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19197

Conjugacy classes & character table

2205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19197, 160);