Finite Group DatabasebetaFinite Group Databasebeta| order | 25100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D25×D251 |
| unambiguous semidirect product | (D25×C251)⋊C2 |
| unambiguous semidirect product | (C25×D251)⋊C2 |
| unambiguous semidirect product | D6275⋊C2 |
| Fitting, derived, Hall | C25×C251 ⋊ C22 |
| Sylow | C251 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D251 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C251 | C22 |
| Frattini | C5 | D5×D251 |
| socle | C5×C251 | C2×D5 |
| LCS | G ▷ C25×C251 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6275 |
1778 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25100, 12);