Finite Group DatabasebetaFinite Group Databasebeta| order | 4284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D119 |
| Fitting, socle, derived, Hall | C32×C7×C17 ⋊ C22 |
| Hall | C32×C17 ⋊ C2×D7 |
| Hall | C7×C17 ⋊ D32 |
| Hall | C32×C7 ⋊ C2×D17 |
| Sylow | C17 ⋊ (C3⋊D3)⋊D7 |
| Sylow | C32 ⋊ C2×D119 |
| Sylow | C7 ⋊ (C3⋊D3)⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C17 | C22 |
| LCS | G ▷ C32×C7×C17 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
Polycyclic presentation:
2^2,3^2,7,17|d^a=d^2,e^a=e^6,f^a=f^16,c^b=c^2,d^b=d^2363 conjugacy classes — view the full character table.
| maximal subgroup of | C5×(C3⋊D3)⋊D119, #36339512, (C3⋊D3)⋊D595, … |
| maximal normal subgroup of | C5×(C3⋊D3)⋊D119, C7×(C3⋊D3)⋊D119 |
| maximal quotient of | C5×(C3⋊D3)⋊D119, #36339512, (C3⋊D3)⋊D595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4284, 109);