Finite Group DatabasebetaFinite Group Databasebeta| order | 8602 |
| automorphism | Aut(G) order 15139520 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4301 |
| unambiguous semidirect product | C11⋊D391 |
| unambiguous semidirect product | C17⋊D253 |
| unambiguous semidirect product | C23⋊D187 |
| Fitting, socle, derived, Hall | C11×C17×C23 ⋊ C2 |
| Hall | C17×C23 ⋊ D11 |
| Hall | C11×C23 ⋊ D17 |
| Hall | C11×C17 ⋊ D23 |
| Sylow | C23 ⋊ D187 |
| Sylow | C17 ⋊ D253 |
| Sylow | C11 ⋊ D391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C17×C23 | C2 |
| LCS | G ▷ C11×C17×C23 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,17,23|b^a=b^10,c^a=c^16,d^a=d^222152 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D187, D17×D253, D11×D391, … |
| maximal normal subgroup of | D23×D187, D17×D253, D11×D391, … |
| maximal quotient of | Dic4301, C2×D4301, C3×D4301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8602, 9);