Finite Group DatabasebetaFinite Group Databasebeta| order | 26004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C11×D197 |
| unambiguous semidirect product | C197⋊(C22×C3×C11) |
| unambiguous semidirect product | (C2×C197)⋊(C2×C3×C11) |
| Fitting, socle | C2×C3×C11×C197 ⋊ C2 |
| derived, Sylow | C197 ⋊ C22×C3×C11 |
| Hall | C3×C11×C197 ⋊ C22 |
| Hall | C11×C197 ⋊ C22×C3 |
| Hall | C3×C197 ⋊ C22×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C11 | D197 |
| commutator, cosocle, hypocenter | C197 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C11×C197 | C2 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C2×C3×C11 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13002 |
6600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26004, 22);