Finite Group DatabasebetaFinite Group Databasebeta| order | 4980 |
| automorphism | Aut(G) order 1633440 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1245 |
| unambiguous semidirect product | C3⋊Dic415 |
| unambiguous semidirect product | C83⋊Dic15 |
| derived, Hall | C3×C5×C83 ⋊ C4 |
| Hall | C5×C83 ⋊ Dic3 |
| Hall | C3×C83 ⋊ Dic5 |
| Sylow | C83 ⋊ Dic15 |
| Hall | C3×C5 ⋊ Dic83 |
| Sylow | C5 ⋊ Dic249 |
| Sylow | C3 ⋊ Dic415 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1245 |
| commutator, hypocenter | C3×C5×C83 | C4 |
| Fitting, socle | C2×C3×C5×C83 | C2 |
| LCS | G ▷ C3×C5×C83 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,83,2|a^2=e,b^a=b^2,c^a=c^4,d^a=d^821248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3735, C3×Dic1245, C3⋊Dic1245, … |
| maximal normal subgroup of | C3×Dic1245, C5×Dic1245, C7×Dic1245, … |
| maximal quotient of | Dic3735, C3×Dic1245, C3⋊Dic1245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4980, 8);