Finite Group DatabasebetaFinite Group Databasebeta| order | 4978 |
| automorphism | Aut(G) order 5824260 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2489 |
| unambiguous semidirect product | C19⋊D131 |
| unambiguous semidirect product | C131⋊D19 |
| Fitting, socle, derived, Hall | C19×C131 ⋊ C2 |
| Sylow | C131 ⋊ D19 |
| Sylow | C19 ⋊ D131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C131 | C2 |
| LCS | G ▷ C19×C131 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,131|b^a=b^18,c^a=c^1301246 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2489, D7467, (C19⋊C3)⋊D131, … |
| maximal normal subgroup of | C3×D2489, (C19⋊C3)⋊D131, C5×D2489, … |
| maximal quotient of | C3×D2489, D7467, C5×D2489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4978, 3);