Finite Group Databasebeta

C3×#21463361 #37555941

order23571
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC3×#21463361

Splittings

SylowC97 ⋊ C3×#731

Subgroups

subgroupG/H
centerC32C32⋊(C97⋊C3)
commutator, cosocleC32×C97C33
FrattiniC32C32×C97⋊C3
Fitting, prime radicalC3×H(3,𝔽3)×C97C3
socleC32×C97H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C97⋊C3
hypocenterC97C3×#731
LCSG ▷ C32×C97 ▷ C3×C97 ▷ C97
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7857

Conjugacy classes & character table

1107 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23571, 248);