Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4070 |
| Sylow | C5 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 143 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);(1,2)(12,14,15,19)(13,16,17,18);(4,6)(8,9)(10,11)(12,13,15,17)(14,18,19,16);(1,2)92 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#64672, #10600238, #10600250, … |
| maximal normal subgroup of | C2×#64672, #10600238, #10600250, … |
| maximal quotient of | C2×#65222, C2×#65217, C2×#65218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1456);