Finite Group DatabasebetaFinite Group Databasebeta| order | 24804 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×#261⋊C9 |
| unambiguous semidirect product | #261⋊(C9×C53) |
| unambiguous semidirect product | (#261×C53)⋊C9 |
| derived, Sylow | C13 ⋊ C4×C9×C53 |
| Hall | C53×C13⋊C9 ⋊ C4 |
| Hall | #261×C53 ⋊ C9 |
| Hall | C13×C53 ⋊ C4×C9 |
| Hall | C13⋊C9 ⋊ C4×C53 |
| Hall | #261 ⋊ C9×C53 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6201 |
2067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24804, 26);