Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #342 |
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 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 — 2 generators on 17 points:
(1,2,4,5,3)(10,12)(11,14,15,16)(13,17);(2,3)(4,5)(6,7,8,9)(10,11)(12,16)(13,15)(14,17)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,b^a=be,d^a=df,g^a=g^4,e^b=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊#2104, #10599744, #10599746, … |
| maximal normal subgroup of | C5⋊#2104, #10599744, #10599746, … |
| maximal quotient of | #10598103, #10598108, #10598109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 85);