Finite Group DatabasebetaFinite Group Databasebeta| order | 17006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D773 |
| unambiguous semidirect product | C773⋊(C2×C11) |
| Fitting, socle, Hall | C11×C773 ⋊ C2 |
| derived, Sylow | C773 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D773 |
| commutator, cosocle, hypocenter | C773 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C773 | C2 |
| LCS | G ▷ C773 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8503 |
4268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#15690586, C11⋊#15690586, D11×D773, … |
| maximal normal subgroup of | C11×#15690586, C11⋊#15690586, D11×D773, … |
| maximal quotient of | C11×Dic773, C2×C11×D773 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17006, 2);