Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4097 |
| Sylow | C5 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 23 points:
(3,4,6,7,5)(8,10)(9,13)(11,20)(12,17)(14,23)(15,22)(16,19)(18,21);(1,2)(10,17)(13,22)(16,23)(18,20);(4,5)(6,7)(8,9,12,15)(10,16,17,23)(11,19,21,14)(13,20,22,18);(1,2)62 conjugacy classes — view the full character table.
| maximal subgroup of | #10600797, #10600800, #10600801, … |
| maximal normal subgroup of | #10600797, #10600800, #10600801, … |
| maximal quotient of | C2×#65284, C2×#65293, C2×#65285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1495);