Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D85 |
| Fitting, socle, derived, Hall | C3×C52×C17 ⋊ C22 |
| Hall | C52×C17 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ D52 |
| Sylow | C52 ⋊ D3×D17 |
| Sylow | C17 ⋊ D15⋊D5 |
| Sylow | C3 ⋊ D5×D85 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C17 | C22 |
| LCS | G ▷ C3×C52×C17 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,17|d^a=d^4,e^a=e^4,f^a=f^16,c^b=c^2,d^b=d^4390 conjugacy classes — view the full character table.
| maximal subgroup of | #90646⋊D17, D45⋊D85, #29505891, … |
| maximal normal subgroup of | C3×D15⋊D85, C7×D15⋊D85 |
| maximal quotient of | D45⋊D85, C3×D15⋊D85, #29506019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 134);