Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#104 ⋊ C2 |
| Sylow | C5 ⋊ #444 |
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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)(6,9,10,19,11,18,20,8)(7,13,14,21,16,12,15,17);(6,8)(7,12)(9,10)(11,19)(13,16)(14,17)(15,21)(18,20);(2,3)(4,5)(6,7)(8,17)(9,13)(10,14)(11,16)(12,18)(15,20)(19,21)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^4,c^b=ce,e^b=ef,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65112, #10610711, #10610720, … |
| maximal normal subgroup of | C2×#65112, #10610711, #10610720, … |
| maximal quotient of | #10598943, #10598944, #10598945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 450);