Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1925 |
| unambiguous semidirect product | C7⋊(C7×D275) |
| unambiguous semidirect product | C11⋊(C7×D175) |
| unambiguous semidirect product | C25⋊(C7×D77) |
| Fitting, Hall | C72×C11×C25 ⋊ C2 |
| derived | C7×C11×C25 ⋊ C2×C7 |
| Hall | C72×C25 ⋊ D11 |
| Hall | C72×C11 ⋊ D25 |
| Hall | C11×C25 ⋊ C7×D7 |
| Sylow | C72 ⋊ D275 |
| Sylow | C25 ⋊ C7×D77 |
| Sylow | C11 ⋊ C7×D175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1925 |
| commutator, cosocle, hypocenter | C7×C11×C25 | C2×C7 |
| Frattini | C5 | C7×D385 |
| Fitting | C72×C11×C25 | C2 |
| socle | C5×C72×C11 | D5 |
| LCS | G ▷ C7×C11×C25 | |
| UCS | C1 ◁ C7 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3850 |
6748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 48);