Finite Group DatabasebetaFinite Group Databasebeta| order | 2550 |
| isoclinism | isoclinic class of C17⋊#3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊#3874 |
| Fitting, socle, Hall | C52×C17 ⋊ D3 |
| derived, Hall | C17×C52⋊C3 ⋊ C2 |
| Hall | C52⋊C3 ⋊ D17 |
| Sylow | C52 ⋊ D51 |
| Sylow | C17 ⋊ #3874 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C17×C52⋊C3 | C2 |
| Fitting, socle | C52×C17 | D3 |
| LCS | G ▷ C17×C52⋊C3 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 255 |
Polycyclic presentation:
2,3,17,5^2|b^a=b^2,c^a=c^16,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^2101 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C17⋊#3874, C7⋊(C17⋊#3874), C11×C17⋊#3874, … |
| maximal normal subgroup of | C7×C17⋊#3874, C11×C17⋊#3874, C13×C17⋊#3874 |
| maximal quotient of | C7×C17⋊#3874, C7⋊(C17⋊#3874), C11×C17⋊#3874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2550, 11);