Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | Aut(G) order 1632000 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1275 |
| unambiguous semidirect product | C3⋊Dic425 |
| derived, Hall | C3×C17×C25 ⋊ C4 |
| Hall | C17×C25 ⋊ Dic3 |
| Hall | C3×C25 ⋊ Dic17 |
| Hall | C3×C17 ⋊ Dic25 |
| Sylow | C25 ⋊ Dic51 |
| Sylow | C17 ⋊ Dic75 |
| Sylow | C3 ⋊ Dic425 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1275 |
| commutator, hypocenter | C3×C17×C25 | C4 |
| Frattini | C2×C5 | D255 |
| Fitting | C2×C3×C17×C25 | C2 |
| socle | C2×C3×C5×C17 | D5 |
| LCS | G ▷ C3×C17×C25 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,17,2,5|a^2=e,c^5=f^4,b^a=b^2,c^a=c^4f,d^a=d^16,f^a=f^41278 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3825, C3×Dic1275, C3⋊Dic1275, … |
| maximal normal subgroup of | C3×Dic1275, C7×Dic1275, Dic2550 |
| maximal quotient of | Dic3825, C3×Dic1275, C3⋊Dic1275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 8);