Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D85⋊D15 |
| 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 ⋊ D5×D15 |
| Sylow | C3 ⋊ (C5⋊D5)⋊D17 |
| 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,f^a=f^16,c^b=c^2,d^b=d^4,e^b=e^4348 conjugacy classes — view the full character table.
| maximal subgroup of | D85⋊D45, #29505888, C3×D85⋊D15, … |
| maximal normal subgroup of | C3×D85⋊D15, C7×D85⋊D15 |
| maximal quotient of | D85⋊D45, C3×D85⋊D15, D85⋊(C3⋊D15), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 131);