Finite Group DatabasebetaFinite Group Databasebeta| order | 26026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C132 · Schur multiplier (H2) = C13 |
| direct product | C7×C132×D11 |
| unambiguous semidirect product | C11⋊(C2×C7×C132) |
| Fitting, socle, Hall | C7×C11×C132 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C7×C132 |
| Hall | C11×C132 ⋊ C2×C7 |
| Hall | C7×C11 ⋊ C2×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C132 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C7×C132 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C132 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C7×C132 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13013 |
8281 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26026, 18);