Finite Group DatabasebetaFinite Group Databasebeta| order | 8602 |
| isoclinism | isoclinic class of D187 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D187 |
| unambiguous semidirect product | C11⋊(C23×D17) |
| unambiguous semidirect product | C17⋊(D11×C23) |
| Fitting, socle, Hall | C11×C17×C23 ⋊ C2 |
| derived, Hall | C11×C17 ⋊ C2×C23 |
| Hall | C17×C23 ⋊ D11 |
| Hall | C11×C23 ⋊ D17 |
| Sylow | C17 ⋊ D11×C23 |
| Sylow | C11 ⋊ C23×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D187 |
| commutator, hypocenter | C11×C17 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C23 | C2 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
2185 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D187, D11×C23×D17, D187⋊D23, … |
| maximal normal subgroup of | D23×D187, D11×C23×D17, D187⋊D23, … |
| maximal quotient of | C23×Dic187, C2×C23×D187, C3×C23×D187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8602, 8);