Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D5⋊(C22⋊C8) |
| Sylow | C5 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 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 — 3 generators on 17 points:
(1,2,3,5,4)(10,12,14,13)(11,15,17,16);(7,9);(2,3,4,5)(6,7)(8,9)(10,11,13,16,14,17,12,15)Polycyclic presentation:
2^6,5|a^2=d,c^2=f,d^2=f,b^a=be,g^a=g^2,g^d=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10598504, #10598506, #10598551, … |
| maximal normal subgroup of | #10598504, #10598506, #10598551, … |
| maximal quotient of | #10604160, #10604161, #10604171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1091);