Finite Group DatabasebetaFinite Group Databasebeta| order | 26268 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C199⋊C11 |
| unambiguous semidirect product | C3⋊(C4×C199⋊C11) |
| unambiguous semidirect product | (Dic3×C199)⋊C11 |
| derived, Hall | C3×C199 ⋊ C4×C11 |
| Hall | C3×C199⋊C11 ⋊ C4 |
| Hall | Dic3×C199 ⋊ C11 |
| Sylow | C199 ⋊ C11×Dic3 |
| Sylow | C3 ⋊ C4×C199⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C199⋊C11 |
| commutator, hypocenter | C3×C199 | C4×C11 |
| Fitting, socle, cosocle | C2×C3×C199 | C2×C11 |
| prime radical | C2×C3×C199⋊C11 | C2 |
| LCS | G ▷ C3×C199 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2388 |
174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26268, 13);