Finite Group Databasebeta

C3×C32⋊(C97⋊C9) #37555851

order23571
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productC3×C32⋊(C97⋊C9)

Splittings

SylowC97 ⋊ C3×C32⋊C9

Subgroups

subgroupG/H
centerC33C3×C97⋊C3
commutatorC3×C97C32×C9
FrattiniC32C32×C97⋊C3
Fitting, prime radicalC34×C97C3
socleC33×C97C32
cosocleC32×C97C33
hypercenterC34C97⋊C3
hypocenterC97C3×C32⋊C9
LCSG ▷ C3×C97 ▷ C97
UCSC1 ◁ C33 ◁ C34

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7857

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23571, 158);