Finite Group DatabasebetaFinite Group Databasebeta| order | 26026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C7⋊(C11⋊(C13⋊D13)) |
| unambiguous semidirect product | C11⋊(C7⋊(C13⋊D13)) |
| unambiguous semidirect product | C13⋊D1001 |
| Fitting, socle, derived, Hall | C7×C11×C132 ⋊ C2 |
| Hall | C11×C132 ⋊ D7 |
| Hall | C7×C132 ⋊ D11 |
| Sylow | C132 ⋊ D77 |
| Hall | C7×C11 ⋊ C13⋊D13 |
| Sylow | C11 ⋊ C7⋊(C13⋊D13) |
| Sylow | C7 ⋊ C11⋊(C13⋊D13) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C132 | C2 |
| LCS | G ▷ C7×C11×C132 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13013 |
Polycyclic presentation:
2,7,11,13^2|b^a=b^6,c^a=c^10,d^a=d^12,e^a=e^126508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26026, 26);