Finite Group DatabasebetaFinite Group Databasebeta| order | 8398 |
| automorphism | Aut(G) order 14511744 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4199 |
| unambiguous semidirect product | C13⋊D323 |
| unambiguous semidirect product | C17⋊D247 |
| unambiguous semidirect product | C19⋊D221 |
| Fitting, socle, derived, Hall | C13×C17×C19 ⋊ C2 |
| Hall | C17×C19 ⋊ D13 |
| Hall | C13×C19 ⋊ D17 |
| Hall | C13×C17 ⋊ D19 |
| Sylow | C19 ⋊ D221 |
| Sylow | C17 ⋊ D247 |
| Sylow | C13 ⋊ D323 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C17×C19 | C2 |
| LCS | G ▷ C13×C17×C19 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,17,19|b^a=b^12,c^a=c^16,d^a=d^182101 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D221, D17×D247, D13×D323, … |
| maximal normal subgroup of | D19×D221, D17×D247, D13×D323, … |
| maximal quotient of | Dic4199, C2×D4199, C3×D4199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8398, 8);