Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#137 ⋊ C2 |
| Sylow | C5 ⋊ #456 |
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 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)(6,9,12,13)(7,14,16,21)(8,17,18,15)(10,20,11,19);(6,8,12,18)(7,13,16,9)(10,14,11,21)(15,20,17,19);(2,3)(4,5)(6,7)(8,13)(9,18)(10,17)(11,15)(12,16)(14,19)(20,21)Polycyclic presentation:
2^6,5|b^2=f,c^2=f,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,e^b=ef,d^c=df,e^c=ef38 conjugacy classes — view the full character table.
| maximal subgroup of | #10612022, #10612024, D5×#456, … |
| maximal normal subgroup of | #10612022, #10612024, D5×#456, … |
| maximal quotient of | #10601090, #10601101, #10601102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 832);