Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ #450 |
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 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) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(7,9)(10,11,13,15)(12,17,16,14);(11,14)(12,16)(15,17);(2,3)(4,5)(6,7)(8,9)Polycyclic presentation:
2^6,5|c^2=f,e^2=f,c^a=cd,g^a=g^4,c^b=ce,e^b=ef,e^c=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | #10611382, #10611385, #10611390, … |
| maximal normal subgroup of | #10611382, #10611385, #10611390, … |
| maximal quotient of | #10600962, #10600991, #10601000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 796);