Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4013 |
| Sylow | C5 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 15 points:
(3,4,5,7,6)(9,12)(10,14);(4,5,6,7)(8,9,10,13,11,12,14,15);(1,2)38 conjugacy classes — view the full character table.
| maximal subgroup of | #10598709, #10598822, C2×#64864, … |
| maximal normal subgroup of | #10598709, #10598822, C2×#64864, … |
| maximal quotient of | C2×#64915, #10604879, #10604880, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1137);