Finite Group DatabasebetaFinite Group Databasebeta| order | 17182 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C71 · Schur multiplier (H2) = C1 |
| direct product | C11×D11×C71 |
| unambiguous semidirect product | C11⋊(C2×C11×C71) |
| Fitting, socle, Hall | C112×C71 ⋊ C2 |
| derived | C11 ⋊ C2×C11×C71 |
| Sylow | C112 ⋊ C2×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C71 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C11×C71 |
| Frattini | C1 | G |
| Fitting, socle | C112×C71 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C11×C71 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1562 |
5467 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D71, D112×C71, D11×D781, … |
| maximal normal subgroup of | C11×D11×D71, D112×C71, D11×D781, … |
| maximal quotient of | C11×Dic11×C71, C2×C11×D11×C71 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17182, 9);