Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D1925 |
| unambiguous semidirect product | C11⋊(C7⋊D175) |
| unambiguous semidirect product | C25⋊(C7⋊D77) |
| Fitting, derived, Hall | C72×C11×C25 ⋊ C2 |
| 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 | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C72×C11×C25 | C2 |
| Frattini | C5 | C5⋊(C7⋊D77) |
| socle | C5×C72×C11 | D5 |
| LCS | G ▷ C72×C11×C25 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
Polycyclic presentation:
2,5,7^2,11,5|b^5=f^4,b^a=b^4f,c^a=c^6,d^a=d^6,e^a=e^10,f^a=f^46739 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 50);