Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D2695 |
| unambiguous semidirect product | C11⋊(C5⋊D245) |
| unambiguous semidirect product | C49⋊(C5⋊D55) |
| Fitting, derived, Hall | C52×C11×C49 ⋊ C2 |
| Hall | C52×C49 ⋊ D11 |
| Hall | C11×C49 ⋊ C5⋊D5 |
| Hall | C52×C11 ⋊ D49 |
| Sylow | C49 ⋊ C5⋊D55 |
| Sylow | C52 ⋊ D539 |
| Sylow | C11 ⋊ C5⋊D245 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C11×C49 | C2 |
| Frattini | C7 | C5⋊D385 |
| socle | C52×C7×C11 | D7 |
| LCS | G ▷ C52×C11×C49 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
Polycyclic presentation:
2,5^2,7,11,7|d^7=f^6,b^a=b^4,c^a=c^4,d^a=d^6f,e^a=e^10,f^a=f^66739 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 32);