Finite Group DatabasebetaFinite Group Databasebeta| order | 4966 |
| automorphism | Aut(G) order 5661240 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2483 |
| unambiguous semidirect product | C13⋊D191 |
| unambiguous semidirect product | C191⋊D13 |
| Fitting, socle, derived, Hall | C13×C191 ⋊ C2 |
| Sylow | C191 ⋊ D13 |
| Sylow | C13 ⋊ D191 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C191 | C2 |
| LCS | G ▷ C13×C191 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,191|b^a=b^12,c^a=c^1901243 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2483, D7449, (C13⋊C3)⋊D191, … |
| maximal normal subgroup of | C3×D2483, (C13⋊C3)⋊D191, C5×D2483, … |
| maximal quotient of | C3×D2483, D7449, C5×D2483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4966, 3);