Finite Group DatabasebetaFinite Group Databasebeta| order | 4284 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C3 |
| direct product | C7×C17×#157 |
| Fitting, socle, Hall | C32×C7×C17 ⋊ C4 |
| derived, Sylow | C32 ⋊ C4×C7×C17 |
| Hall | C32×C17 ⋊ C4×C7 |
| Hall | C32×C7 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C17 | #157 |
| commutator, hypocenter | C32 | C4×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C17 | C4 |
| prime radical | C7×C17×C3⋊D3 | C2 |
| cosocle | C3⋊D3 | C2×C7×C17 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C7×C17 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 714 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)(25,26)(27,29,30,28);(25,27,30)(26,29,28)714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×C17×#157, C7×C17×#4380, C7×C17×#4379, … |
| maximal normal subgroup of | C5×C7×C17×#157, C17×#157×C49, C72×C17×#157 |
| maximal quotient of | C5×C7×C17×#157, C7×C17×#4380, C7×C17×#4379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4284, 110);