Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4025 |
| Sylow | C5 ⋊ C2×#126 |
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 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:
(1,2)(3,4,6,7,5)(8,10)(9,12)(11,15)(13,14)(16,18)(17,20)(19,22)(21,23);(10,15)(12,14)(16,18,19,22)(17,20,21,23);(4,5)(6,7)(8,9,11,13)(10,14,15,12)(16,17,19,21)(18,20,22,23);(1,2)68 conjugacy classes — view the full character table.
| maximal subgroup of | #10598898, #10604209, #10604210, … |
| maximal normal subgroup of | #10598898, #10604209, #10604210, … |
| maximal quotient of | C2×#64940, C2×#64941, C2×#64942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1154);