Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D539 |
| unambiguous semidirect product | C49⋊(C52×D11) |
| Fitting, Hall | C52×C11×C49 ⋊ C2 |
| derived, Hall | C11×C49 ⋊ C2×C52 |
| Hall | C52×C49 ⋊ D11 |
| Hall | C52×C11 ⋊ D49 |
| Sylow | C49 ⋊ C52×D11 |
| Sylow | C11 ⋊ C52×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D539 |
| commutator, cosocle, hypocenter | C11×C49 | C2×C52 |
| Frattini | C7 | C52×D77 |
| Fitting | C52×C11×C49 | C2 |
| socle | C52×C7×C11 | D7 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
6775 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 24);