Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4053 |
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#131 |
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 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)(8,10,11,17,12,16,18,22)(9,14,15,21,13,19,20,23);(1,2)(9,13)(10,16)(15,20)(17,22);(4,5)(6,7)(8,9)(10,14)(11,15)(12,13)(16,19)(17,21)(18,20)(22,23);(1,2)80 conjugacy classes — view the full character table.
| maximal subgroup of | #10599503, #10599517, #10599532, … |
| maximal normal subgroup of | #10599503, #10599517, #10599532, … |
| maximal quotient of | C2×#64990, #10610212, C2×#64997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1416);