Finite Group DatabasebetaFinite Group Databasebeta| order | 16764 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C11×C127 ⋊ C22×C3 |
| Hall | D11×D127 ⋊ C3 |
| Hall | C11×C127⋊C3 ⋊ C22 |
| Hall | C127⋊C3 ⋊ C2×D11 |
| Sylow | C127 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ C2×D127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C127 | C22×C3 |
| LCS | G ▷ C11×C127 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1397 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16764, 14);