Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#107 ⋊ C2 |
| Sylow | C5 ⋊ #468 |
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(11,15)(12,17)(14,16);(10,11,12,16,13,14,17,15);(2,3)(4,5)(7,9)(11,14)(15,16)Polycyclic presentation:
2^6,5|b^2=e,c^2=d,e^2=f,b^a=bf,c^a=cd,g^a=g^4,c^b=ce,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65175, #10610881, #10610889, … |
| maximal normal subgroup of | C2×#65175, #10610881, #10610889, … |
| maximal quotient of | #10599375, #10599376, #10599377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 513);