Finite Group DatabasebetaFinite Group Databasebeta| order | 4284 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C9⋊#595) |
| unambiguous semidirect product | C9⋊(C7⋊#595) |
| Fitting, derived, Hall | C7×C9×C17 ⋊ C4 |
| Hall | C9×C17 ⋊ Dic7 |
| Hall | C7×C17 ⋊ Dic9 |
| Hall | C7×C9 ⋊ #595 |
| Sylow | C17 ⋊ Dic63 |
| Sylow | C9 ⋊ C7⋊#595 |
| Sylow | C7 ⋊ C9⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C9×C17 | C4 |
| Frattini | C3 | C3⋊(C7⋊#595) |
| socle | C3×C7×C17 | Dic3 |
| prime radical | C3×C7×D17 | D3 |
| cosocle | C7×C9×D17 | C2 |
| LCS | G ▷ C7×C9×C17 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1071 |
Polycyclic presentation:
2^2,3,7,17,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^6,e^a=e^13,f^a=f^2,e^b=e^16318 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7⋊(C9⋊#595), C7⋊(C9⋊#66775), C7⋊(C9⋊#66776), … |
| maximal normal subgroup of | C5×C7⋊(C9⋊#595), C7×C7⋊(C9⋊#595) |
| maximal quotient of | C5×C7⋊(C9⋊#595), C7⋊(C9⋊#66775), C7⋊(C9⋊#66776), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4284, 23);