Finite Group DatabasebetaFinite Group Databasebeta| order | 26026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C13 |
| direct product | C11×C7⋊(C13⋊D13) |
| unambiguous semidirect product | C7⋊(C11×C13⋊D13) |
| unambiguous semidirect product | C13⋊(C11×D91) |
| Fitting, socle, Hall | C7×C11×C132 ⋊ C2 |
| derived, Hall | C7×C132 ⋊ C2×C11 |
| Hall | C11×C132 ⋊ D7 |
| Sylow | C132 ⋊ C11×D7 |
| Hall | C7×C11 ⋊ C13⋊D13 |
| Sylow | C7 ⋊ C11×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C7⋊(C13⋊D13) |
| commutator, cosocle, hypocenter | C7×C132 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C132 | C2 |
| LCS | G ▷ C7×C132 | |
| UCS | C1 ◁ C11 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13013 |
6523 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26026, 23);