Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×D5⋊M16 |
| unambiguous semidirect product | D5⋊(C7×M16) |
| Hall | C5×C7 ⋊ C2×M16 |
| Sylow | C5 ⋊ C2×C7×M16 |
136 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 72 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 — 3 generators on 20 points:
(1,2,3,4,5,6,7)(8,9,10,12,11)(14,19)(18,20);(13,15,17,16)(14,18,19,20);(9,10,11,12)(13,14,16,20,17,19,15,18)196 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×D5⋊M16, C7×M16×AGL(1,𝔽5), #72218203, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×D5⋊M16, C7×M16×AGL(1,𝔽5), #72218203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 950);