Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D5×SD16 |
| Fitting | C2×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ C22×SD16 |
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:
(1,2)(3,4,6,7,5)(9,12)(10,15)(13,14);(1,2)(8,9,11,14)(10,12,15,13);(4,5)(6,7);(1,2)56 conjugacy classes — view the full character table.
| maximal subgroup of | #10604817, #10604818, #10604822, … |
| maximal normal subgroup of | #10604817, #10604818, #10604822, … |
| maximal quotient of | C2×#65047, C2×#65050, C2×#65049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1430);