Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C5 ⋊ #453 |
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 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) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2,4,5,3)(7,10)(8,13)(11,12);(6,7)(8,10)(9,11)(12,13);(2,3)(4,5)(8,13)(10,12)Polycyclic presentation:
2^6,5|e^2=f,c^a=cd,e^a=ef,g^a=g^4,c^b=ce,d^b=df,e^b=ef,e^c=ef38 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#453, #10612009, #10612015, … |
| maximal normal subgroup of | D5×#453, #10612009, #10612015, … |
| maximal quotient of | #10601090, #10601098, #10601099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 825);