Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C49⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | C49⋊(C5⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C11⋊C5)⋊D245 |
| unambiguous semidirect product | D2695⋊C5 |
| Fitting, derived | C5×C11×C49 ⋊ C2×C5 |
| Hall | C5×C49×C11⋊C5 ⋊ C2 |
| Hall | C11×C49 ⋊ C5×D5 |
| Hall | C5×C11⋊C5 ⋊ D49 |
| Sylow | C49 ⋊ C5⋊AGL(1,𝔽11) |
| Sylow | C11 ⋊ C5×D245 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C11×C49 | C2×C5 |
| Frattini | C7 | C5⋊(C7⋊AGL(1,𝔽11)) |
| socle | C5×C7×C11 | C5×D7 |
| LCS | G ▷ C5×C11×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2695 |
Polycyclic presentation:
2,5^2,7,11,7|d^7=f^6,c^a=c^4,d^a=d^6f,e^a=e^10,f^a=f^6,e^b=e^4865 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 19);