Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #482 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(8,12)(10,13)(15,20)(16,17)(19,21);(6,8)(7,10)(9,12)(11,13)(14,16,18,17)(15,19,21,20);(2,3)(4,5)(6,7,9,11)(8,10,12,13)(14,15,18,21)(16,19,17,20)Polycyclic presentation:
2^6,5|a^2=e,b^2=f,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10611723, #10611724, #10611741, … |
| maximal normal subgroup of | #10611723, #10611724, #10611741, … |
| maximal quotient of | #10600296, #10600299, #10600300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 662);