Finite Group Databasebeta

C3×C32⋊(C79⋊C9) #34063229

order19197
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productC3×C32⋊(C79⋊C9)

Splittings

SylowC79 ⋊ C3×C32⋊C9

Subgroups

subgroupG/H
centerC33C3×C79⋊C3
commutatorC3×C79C32×C9
FrattiniC32C32×C79⋊C3
Fitting, prime radicalC34×C79C3
socleC33×C79C32
cosocleC32×C79C33
hypercenterC34C79⋊C3
hypocenterC79C3×C32⋊C9
LCSG ▷ C3×C79 ▷ C79
UCSC1 ◁ C33 ◁ C34

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6399

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, 158);