Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C5×#107 ⋊ C2 |
| Sylow | C5 ⋊ #482 |
106 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 106 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) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(7,11)(10,13)(14,16,21,15,18,20,17,19);(6,8,9,12)(7,10,11,13)(14,15)(16,21)(17,20)(18,19);(2,3)(4,5)(6,7)(8,10)(9,11)(12,13)(15,19)(16,20)Polycyclic presentation:
2^6,5|b^2=d,c^2=ef,e^2=f,b^a=bf,c^a=cdf,g^a=g^4,c^b=ce,e^b=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65174, #10610872, #10610888, … |
| maximal normal subgroup of | C2×#65174, #10610872, #10610888, … |
| maximal quotient of | #10599585, #10599606, #10599612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 512);