Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #435 |
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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:
(1,2,3,5,4)(7,9)(10,12,14,13)(11,16,17,15);(6,7)(8,9)(10,12,14,13)(11,15,17,16);(2,3,4,5)(10,11,13,16,14,17,12,15)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=f,d^2=f,c^a=cf,g^a=g^2,c^b=ce,g^d=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65704, #10617084, #10617090, … |
| maximal normal subgroup of | C2×#65704, #10617084, #10617090, … |
| maximal quotient of | #10603776, #10603777, #10603785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1042);