Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #450 |
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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:
(1,2,4,5,3)(7,9);(11,14)(12,17)(15,16);(2,3)(4,5)(6,7)(8,9)(10,11,13,16)(12,14,17,15)Polycyclic presentation:
2^6,5|a^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^4,e^b=ef59 conjugacy classes — view the full character table.
| maximal subgroup of | #10600490, #10600491, #10600495, … |
| maximal normal subgroup of | #10600490, #10600491, #10600495, … |
| maximal quotient of | #10602349, #10602352, #10602400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 845);