Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4064 |
| Fitting | C2×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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)(8,10,12,16)(9,13,15,22)(11,20,21,18)(14,23,19,17);(1,2)(8,9,12,15)(10,17,16,23)(11,19,21,14)(13,20,22,18);(4,5)(6,7)(10,16)(13,22)(17,23)(18,20);(1,2)50 conjugacy classes — view the full character table.
| maximal subgroup of | #10604846, #10604851, C4×#4064, … |
| maximal normal subgroup of | #10604846, #10604851, C4×#4064, … |
| maximal quotient of | C2×#65106, C2×#65078, C2×#65080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1436);