Finite Group DatabasebetaFinite Group Databasebeta| order | 16126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D733 |
| unambiguous semidirect product | C733⋊(C2×C11) |
| Fitting, socle, Hall | C11×C733 ⋊ C2 |
| derived, Sylow | C733 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D733 |
| commutator, cosocle, hypocenter | C733 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C733 | C2 |
| LCS | G ▷ C733 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8063 |
4048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#15668640, C11⋊#15668640, D11×D733, … |
| maximal normal subgroup of | C11×#15668640, C11⋊#15668640, D11×D733, … |
| maximal quotient of | C11×Dic733, C2×C11×D733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16126, 2);