Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #461 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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 — 3 generators on 17 points:
(1,2,4,5,3)(7,9)(10,11,13,15)(12,17,16,14);(11,14)(12,16)(15,17);(2,3)(4,5)(6,7,8,9)Polycyclic presentation:
2^6,5|a^2=e,c^2=f,d^2=f,c^a=ce,g^a=g^4,c^b=cd,d^b=df,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10611350, #10611351, #10611359, … |
| maximal normal subgroup of | #10611350, #10611351, #10611359, … |
| maximal quotient of | #10600946, #10600958, #10600964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 789);