Finite Group DatabasebetaFinite Group Databasebeta| order | 23571 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C97⋊#6855 |
| Sylow | C97 ⋊ #6855 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C3×C97⋊C3 |
| commutator | C3×C97 | C92 |
| Fitting | C32×C9×C97 | C3 |
| socle, prime radical, cosocle | C33×C97 | C32 |
| hypercenter | C32×C9 | C97⋊C3 |
| hypocenter | C97 | #6855 |
| LCS | G ▷ C3×C97 ▷ C97 | |
| UCS | C1 ◁ C33 ◁ C32×C9 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23571 |
Polycyclic presentation:
3^5,97|a^3=d,b^3=e,b^a=bc,f^b=f^352691 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23571, 69);