Finite Group DatabasebetaFinite Group Databasebeta| order | 26026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C13 |
| direct product | C11×(C13⋊D13)⋊C7 |
| unambiguous semidirect product | (C13⋊D13)⋊(C7×C11) |
| unambiguous semidirect product | (C11×C13⋊D13)⋊C7 |
| Fitting, socle, Hall | C11×C132 ⋊ C2×C7 |
| derived, Sylow | C132 ⋊ C2×C7×C11 |
| Hall | C11×C132⋊C7 ⋊ C2 |
| Hall | C11×C13⋊D13 ⋊ C7 |
| Hall | C132⋊C7 ⋊ C2×C11 |
| Hall | C13⋊D13 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | (C13⋊D13)⋊C7 |
| commutator, cosocle, hypocenter | C132 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C132 | C2×C7 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1001 |
286 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26026, 11);