Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#123 ⋊ C2 |
| Sylow | C5 ⋊ #458 |
160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 160 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) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,9,10,16)(7,12,13,20)(8,14,15,21)(11,17,18,19);(6,8)(7,11)(9,14)(10,15)(12,19)(13,18)(16,21)(17,20);(2,3)(4,5)(6,7)(8,11)(9,12)(10,13)(14,19)(15,18)(16,20)(17,21)Polycyclic presentation:
2^6,5|c^2=f,c^a=cd,e^a=ef,g^a=g^4,c^b=ce,d^b=df44 conjugacy classes — view the full character table.
| maximal subgroup of | #10599931, #10599932, #10599933, … |
| maximal normal subgroup of | #10599931, #10599932, #10599933, … |
| maximal quotient of | #10600329, #10600331, #10600332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 680);