Finite Group DatabasebetaFinite Group Databasebeta| order | 5092 |
| automorphism | Aut(G) order 3024648 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1273 |
| unambiguous semidirect product | C19⋊Dic67 |
| unambiguous semidirect product | C67⋊Dic19 |
| derived, Hall | C19×C67 ⋊ C4 |
| Sylow | C67 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1273 |
| commutator, hypocenter | C19×C67 | C4 |
| Fitting, socle | C2×C19×C67 | C2 |
| LCS | G ▷ C19×C67 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,67,2|a^2=d,b^a=b^18,c^a=c^661276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1273, Dic3819, (C67⋊C3)⋊Dic19, … |
| maximal normal subgroup of | C3×Dic1273, (C67⋊C3)⋊Dic19, (C19⋊C3)⋊Dic67, … |
| maximal quotient of | C3×Dic1273, Dic3819, C5×Dic1273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5092, 4);