Finite Group DatabasebetaFinite Group Databasebeta| order | 25100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×#20262472⋊C2 |
| unambiguous semidirect product | #20262472⋊C22 |
| unambiguous semidirect product | (C2×#20262472)⋊C2 |
| derived, Sylow | C251 ⋊ C22×C25 |
| Hall | #20262472 ⋊ C22 |
| Hall | C2×D251 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D251⋊C5 |
| commutator, hypocenter | C251 | C22×C25 |
| Frattini | C5 | C2×D251⋊C5 |
| Fitting, socle | C2×C5×C251 | C2×C5 |
| prime radical | C2×C5×D251 | C5 |
| cosocle | C5×C251 | C22×C5 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C2×C5 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12550 |
350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25100, 8);