Finite Group Databasebeta

C3×#21463357 #37555932

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

Aliases

direct productC3×#21463357

Splittings

SylowC97 ⋊ C3×C27⋊C3

Subgroups

subgroupG/H
centerC3×C9C3×C97⋊C3
commutatorC3×C97C32×C9
FrattiniC9C32×C97⋊C3
FittingC32×C9×C97C3
socleC32×C97C3×C9
prime radicalC33×C97C9
cosocleC9×C97C33
hypercenterC32×C9C97⋊C3
hypocenterC97C3×C27⋊C3
LCSG ▷ C3×C97 ▷ C97
UCSC1 ◁ C3×C9 ◁ C32×C9

120 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, 239);