Finite Group DatabasebetaFinite Group Databasebeta| order | 25210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C2521⋊C5 |
| unambiguous semidirect product | (C2×C2521)⋊C5 |
| Fitting, socle, Hall | C2×C2521 ⋊ C5 |
| derived, Sylow | C2521 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C2521⋊C5 |
| commutator, cosocle, hypocenter | C2521 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C2521 | C5 |
| LCS | G ▷ C2521 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5042 |
1018 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25210, 2);