Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #407 |
190 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 58 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:
(1,2,3,5,4)(10,12,14,13)(11,15,16,17);(7,9);(2,3,4,5)(6,7)(8,9)(10,11,13,15,14,16,12,17)Polycyclic presentation:
2^6,5|a^2=d,c^2=f,d^2=f,b^a=be,c^a=cf,g^a=g^2,g^d=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598503, #10598507, #10598555, … |
| maximal normal subgroup of | #10598503, #10598507, #10598555, … |
| maximal quotient of | #10604163, #10604164, #10604172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1094);