Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | D5×#117 |
| Fitting | C5×#117 ⋊ C2 |
| Sylow | C5 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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) = 80 |
A minimal faithful permutation representation — 4 generators on 17 points:
(5,7,8,11)(6,10,9,12)(13,14,16,17,15);(6,9)(10,12);(1,2,3,4)(5,6)(7,10)(8,9)(11,12);(14,15)(16,17)80 conjugacy classes — view the full character table.
| maximal subgroup of | D5×H(3,ℤ/4), D5×#339, #10599546, … |
| maximal normal subgroup of | D5×H(3,ℤ/4), D5×#339, #10599546, … |
| maximal quotient of | #10605113, #10605115, #10605123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1192);