Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5×C7 |
| unambiguous semidirect product | C5⋊(C5⋊(C7⋊D77)) |
| unambiguous semidirect product | C7⋊(C5⋊D385) |
| unambiguous semidirect product | C11⋊(C5⋊(C5⋊(C7⋊D7))) |
| Fitting, socle, derived, Hall | C52×C72×C11 ⋊ C2 |
| Hall | C52×C72 ⋊ D11 |
| Hall | C72×C11 ⋊ C5⋊D5 |
| Hall | C52×C11 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C5⋊D55 |
| Sylow | C52 ⋊ C7⋊D77 |
| Sylow | C11 ⋊ C5⋊(C5⋊(C7⋊D7)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C72×C11 | C2 |
| LCS | G ▷ C52×C72×C11 | |
| UCS | C1 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
Polycyclic presentation:
2,5^2,7^2,11|b^a=b^4,c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^106739 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 80);