Finite Group DatabasebetaFinite Group Databasebeta| order | 25100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×C251⋊C5 |
| unambiguous semidirect product | C5⋊(C22×C251⋊C5) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C251⋊C5) |
| unambiguous semidirect product | (C2×D5×C251)⋊C5 |
| Fitting, socle | C2×C5×C251 ⋊ C2×C5 |
| derived | C5×C251 ⋊ C22×C5 |
| Hall | C5×C251⋊C5 ⋊ C22 |
| Sylow | C251 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C251⋊C5 |
| commutator, cosocle, hypocenter | C5×C251 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C251 | C2×C5 |
| LCS | G ▷ C5×C251 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2510 |
440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25100, 36);