Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4078 |
| Fitting | C22×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 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) = 15 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 4 generators on 15 points:
(3,4,6,7,5)(9,12)(10,15)(13,14);(1,2)(8,10,11,15)(9,12,14,13);(4,5)(6,7)(8,9)(10,12)(11,14)(13,15);(1,2)62 conjugacy classes — view the full character table.
| maximal subgroup of | #10600456, #10600457, #10600869, … |
| maximal normal subgroup of | #10600456, #10600457, #10600869, … |
| maximal quotient of | C2×#65253, C2×#65255, C2×#65257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1465);