Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #408 |
158 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,5,4)(7,9)(12,18)(15,21)(19,24)(22,25);(10,12)(11,15)(13,19)(14,18)(16,22)(17,21)(20,24)(23,25);(2,3,4,5)(6,7)(8,9)(10,11,13,16,14,17,20,23)(12,15,19,22,18,21,24,25)Polycyclic presentation:
2^6,5|a^2=d,d^2=f,c^a=ce,g^a=g^2,c^b=cf,g^d=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598569, #10598574, #10603921, … |
| maximal normal subgroup of | #10598569, #10598574, #10603921, … |
| maximal quotient of | #10604205, #10604207, #10604208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1113);