Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #430 |
102 conjugacy classes of subgroups.
| 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)(6,8,10,18,11,16,9,17)(7,12,13,15,14,20,19,21);(8,16)(12,20)(15,21)(17,18);(2,3)(4,5)(6,7,9,13,11,14,10,19)(8,15,17,20,16,21,18,12)Polycyclic presentation:
2^6,5|a^2=d,c^2=e,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599494, #10599508, #10599511, … |
| maximal normal subgroup of | #10599494, #10599508, #10599511, … |
| maximal quotient of | #10600633, #10600634, #10600635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 752);