Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#104 ⋊ 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)(6,9,10,8,12,16,11,17)(7,13,14,18,15,21,19,20);(6,8,12,17)(7,13,15,21)(9,10,16,11)(14,18,19,20);(2,3)(4,5)(6,7)(8,13)(9,18)(10,19)(11,14)(12,15)(16,20)(17,21)Polycyclic presentation:
2^6,5|b^2=f,c^2=d,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,e^b=ef,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10610717, C2×#65115, #10610726, … |
| maximal normal subgroup of | #10610717, C2×#65115, #10610726, … |
| maximal quotient of | #10598977, #10598978, #10598985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 453);