Finite Group DatabasebetaFinite Group Databasebeta| order | 24980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D1249 |
| unambiguous semidirect product | (D5×C1249)⋊C2 |
| unambiguous semidirect product | (C5×D1249)⋊C2 |
| unambiguous semidirect product | D6245⋊C2 |
| Fitting, socle, derived, Hall | C5×C1249 ⋊ C22 |
| Sylow | C1249 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D1249 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C1249 | C22 |
| LCS | G ▷ C5×C1249 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6245 |
2504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24980, 12);