Finite Group DatabasebetaFinite Group Databasebeta| order | 23571 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C3×C27×C97⋊C3 |
| Fitting | C3×C27×C97 ⋊ C3 |
| derived, Sylow | C97 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | C97⋊C3 |
| commutator, hypocenter | C97 | C32×C27 |
| Frattini | C9 | C32×C97⋊C3 |
| Fitting | C3×C27×C97 | C3 |
| socle | C32×C97 | C3×C9 |
| prime radical | C32×C97⋊C3 | C9 |
| cosocle | C9×C97 | C33 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3×C27 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7857 |
2835 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23571, 234);