Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#108 ⋊ C2 |
| Sylow | C5 ⋊ #471 |
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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)(6,9,10,19,11,20,21,12)(7,13,14,18,16,8,15,17);(6,8,10,17,11,13,21,18)(7,12,15,20,16,19,14,9);(2,3)(4,5)(6,7)(8,12)(9,18)(10,15)(11,16)(13,19)(14,21)(17,20)Polycyclic presentation:
2^6,5|b^2=e,c^2=d,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=cef,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65187, #10610987, #10610992, … |
| maximal normal subgroup of | C2×#65187, #10610987, #10610992, … |
| maximal quotient of | #10599329, #10599330, #10599337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 525);