Finite Group DatabasebetaFinite Group Databasebeta| order | 24900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C83 · Schur multiplier (H2) = C5 |
| direct product | C83×#1039⋊C3 |
| unambiguous semidirect product | #1039⋊(C3×C83) |
| unambiguous semidirect product | (C83×#1039)⋊C3 |
| derived, Sylow | C52 ⋊ C3×C4×C83 |
| Hall | C83×#1039 ⋊ C3 |
| Hall | C52⋊C3×C83 ⋊ C4 |
| Hall | C52×C83 ⋊ C3×C4 |
| Hall | #1039 ⋊ C3×C83 |
| Hall | C52⋊C3 ⋊ C4×C83 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4980 |
1660 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24900, 32);