Finite Group DatabasebetaFinite Group Databasebeta| order | 8702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D229⋊C19 |
| unambiguous semidirect product | (C229⋊C19)⋊C2 |
| Fitting, socle, derived, Sylow | C229 ⋊ C2×C19 |
| Hall | C229⋊C19 ⋊ C2 |
| Hall | D229 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C229 | C2×C19 |
| LCS | G ▷ C229 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,229|c^a=c^228,c^b=c^16544 conjugacy classes — view the full character table.
| maximal subgroup of | #11745021⋊C19, C2×D229⋊C19, C3×D229⋊C19, … |
| maximal normal subgroup of | #11745021⋊C19, C2×D229⋊C19, C3×D229⋊C19, … |
| maximal quotient of | Dic229⋊C19, C2×D229⋊C19, C3×D229⋊C19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8702, 1);