Finite Group DatabasebetaFinite Group Databasebeta| order | 23193 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×C859⋊C3 |
| Fitting | C9×C859 ⋊ C3 |
| derived, Sylow | C859 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C859⋊C3 |
| commutator, hypocenter | C859 | C3×C9 |
| Frattini | C3 | C3×C859⋊C3 |
| Fitting | C9×C859 | C3 |
| socle, cosocle | C3×C859 | C32 |
| prime radical | C3×C859⋊C3 | C3 |
| LCS | G ▷ C859 | |
| UCS | C1 ◁ C9 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7731 |
2601 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23193, 7);