Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4042 |
| Fitting | C2×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 19 points:
(3,4,5,6)(7,8,10,11,9)(13,17)(16,19);(1,2)(4,6)(12,14,15,18)(13,16,17,19);(4,6)(8,9)(10,11)(12,13)(14,16)(15,17)(18,19);(1,2)68 conjugacy classes — view the full character table.
| maximal subgroup of | #10598940, #10604311, #10604338, … |
| maximal normal subgroup of | #10598940, #10604311, #10604338, … |
| maximal quotient of | C2×#64941, C2×#64935, C2×#64946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1180);