Finite Group DatabasebetaFinite Group Databasebeta| order | 23571 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C92×C97 ⋊ C3 |
| Sylow | C97 ⋊ #6900 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C97⋊C3 |
| commutator, socle, cosocle | C32×C97 | C33 |
| Fitting | C92×C97 | C3 |
| prime radical | C32×C97⋊C3 | C32 |
| hypercenter | C92 | C97⋊C3 |
| hypocenter | C97 | #6900 |
| LCS | G ▷ C32×C97 ▷ C97 | |
| UCS | C1 ◁ C32 ◁ C92 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7857 |
Polycyclic presentation:
3^5,97|b^3=d,c^3=e,b^a=bd,c^a=ce,f^a=f^612643 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23571, 231);