Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4024 |
| Sylow | C5 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2)(3,4)(5,6)(7,8,10,11,9)(12,15,16,14)(13,17,18,19);(1,2)(4,6)(12,14)(13,17)(15,16)(18,19);(8,9)(10,11)(12,13,16,18)(14,17,15,19);(1,2)68 conjugacy classes — view the full character table.
| maximal subgroup of | #10599748, #10604208, #10604250, … |
| maximal normal subgroup of | #10599748, #10604208, #10604250, … |
| maximal quotient of | C2×#64943, C2×#64944, C2×#64936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1153);