Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊(C7⋊(D11⋊C25)) |
| unambiguous semidirect product | (C11⋊C25)⋊(C7⋊D7) |
| unambiguous semidirect product | (C7⋊D77)⋊C25 |
| derived, Hall | C72×C11 ⋊ C2×C25 |
| Hall | C72×C11⋊C25 ⋊ C2 |
| Hall | C7⋊D77 ⋊ C25 |
| Hall | C11⋊C25 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D11⋊C25 |
| Sylow | C11 ⋊ C25×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C7⋊(C7⋊AGL(1,𝔽11)) |
| commutator, hypocenter | C72×C11 | C2×C25 |
| Fitting, socle, cosocle | C5×C72×C11 | C2×C5 |
| prime radical | C5×C7⋊D77 | C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
Polycyclic presentation:
2,5,7^2,11,5|b^5=f,c^a=c^6,d^a=d^6,e^a=e^10,e^b=e^4895 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 37);