Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#100 ⋊ C2 |
| Sylow | C5 ⋊ #471 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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)(7,12)(8,14)(9,16)(11,17)(13,19)(18,21);(6,8,9,15,10,14,16,20)(7,11,12,17,13,18,19,21);(2,3)(4,5)(6,7)(8,11)(9,12)(10,13)(14,18)(15,17)(16,19)(20,21)Polycyclic presentation:
2^6,5|b^2=d,d^2=f,c^a=cde,e^a=ef,g^a=g^4,c^b=ce,e^b=ef,d^c=df38 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65037, #10610434, #10610450, … |
| maximal normal subgroup of | C2×#65037, #10610434, #10610450, … |
| maximal quotient of | #10599187, #10599190, #10599191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 375);