Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#102 ⋊ C2 |
| Sylow | C5 ⋊ #481 |
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 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) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(7,11)(10,13)(15,18)(17,21)(19,20);(6,8,9,12)(7,10,11,13)(14,15,16,19)(17,18,21,20);(2,3)(4,5)(6,7)(8,10)(9,11)(12,13)Polycyclic presentation:
2^6,5|b^2=d,e^2=f,c^a=cdf,g^a=g^4,c^b=ce,e^b=ef,e^c=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65066, #10610487, #10610489, … |
| maximal normal subgroup of | C2×#65066, #10610487, #10610489, … |
| maximal quotient of | #10599581, #10599604, #10599609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 404);