Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#4130 |
| unambiguous semidirect product | D5⋊#117 |
| Fitting | C22×C4×C5 ⋊ C4 |
| Sylow | C5 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 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:
(1,2)(3,4,5,7,6)(8,10)(9,12)(11,14)(13,15);(8,9,11,13)(10,12,14,15);(4,5,6,7)(10,14)(12,15);(1,2)56 conjugacy classes — view the full character table.
| maximal subgroup of | #10603909, #10603912, C2×#64863, … |
| maximal normal subgroup of | #10603909, #10603912, C2×#64863, … |
| maximal quotient of | C2×#65678, C2×#65680, D5⋊#431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1592);