Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#711 |
| Fitting | C4×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2,4,5,3)(11,15)(12,16);(10,12,13,16)(11,14,15,17);(2,3)(4,5)(10,11)(12,14)(13,15)(16,17);(6,7,8,9)80 conjugacy classes — view the full character table.
| maximal subgroup of | #10598958, #10598959, #10598966, … |
| maximal normal subgroup of | #10598958, #10598959, #10598966, … |
| maximal quotient of | C4×#4023, C4×#4027, C4×#4032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1208);