Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#4007 |
| Fitting | C5×C7×D4 ⋊ C4 |
| Hall | C5×C7 ⋊ #102 |
| Sylow | C5 ⋊ C7×#102 |
100 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4,5,6,7)(8,9,10,12,11)(14,17)(15,20)(18,19);(9,10,11,12)(13,14)(15,17)(16,19)(18,20)133 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#4007, C7×D8×AGL(1,𝔽5), C7×#65731, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#4007, C7×D8×AGL(1,𝔽5), C7×#65731, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 266);