Finite Group DatabasebetaFinite Group Databasebeta| order | 4284 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C7⋊#10597479 |
| Fitting, socle, derived, Hall | C32×C7×C17 ⋊ C4 |
| Hall | C32×C17 ⋊ Dic7 |
| Hall | C7×C17 ⋊ #157 |
| Hall | C32×C7 ⋊ #595 |
| Sylow | C17 ⋊ C7⋊#157 |
| Sylow | C32 ⋊ C7⋊#595 |
| Sylow | C7 ⋊ #10597479 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C17 | C4 |
| prime radical, cosocle | C7×C3⋊D51 | C2 |
| LCS | G ▷ C32×C7×C17 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
Polycyclic presentation:
2^2,3^2,7,17|a^2=b,c^a=cd,d^a=cd^2,e^a=e^6,f^a=f^13,c^b=c^2,d^b=d^2,f^b=f^16276 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7⋊#10597479, C7⋊#15690390, C7⋊#15690391, … |
| maximal normal subgroup of | C5×C7⋊#10597479, C7×C7⋊#10597479 |
| maximal quotient of | C5×C7⋊#10597479, C7⋊#15690390, C7⋊#15690391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4284, 114);