Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4055 |
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 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) = 23 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 23 points:
(3,4,6,7,5)(8,11,12,19,13,20,10,17)(9,15,14,18,16,23,21,22);(1,2)(8,10,13,12)(9,14,16,21)(11,19,20,17)(15,22,23,18);(4,5)(6,7)(8,9)(10,14)(11,18)(12,21)(13,16)(15,19)(17,23)(20,22);(1,2)62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599500, #10599518, #10599555, … |
| maximal normal subgroup of | #10599500, #10599518, #10599555, … |
| maximal quotient of | C2×#64991, C2×#64999, C2×#65003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1419);