Finite Group DatabasebetaFinite Group Databasebeta| order | 23973 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C131 · Schur multiplier (H2) = C1 |
| direct product | C131×C61⋊C3 |
| unambiguous semidirect product | C61⋊(C3×C131) |
| unambiguous semidirect product | (C61×C131)⋊C3 |
| Fitting, socle, Hall | C61×C131 ⋊ C3 |
| derived, Sylow | C61 ⋊ C3×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C131 | C61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C3×C131 |
| Frattini | C1 | G |
| Fitting, socle | C61×C131 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C131 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7991 |
3013 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23973, 1);