Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #473 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,4,5,3)(6,9)(7,14)(8,19)(10,26)(11,24)(12,25)(13,27)(15,31)(16,23)(17,30)(18,32)(20,36)(21,34)(22,35)(28,37)(29,33);(6,8,10,20,12,22,11,21)(7,13,15,28,17,29,16,18)(9,19,26,36,25,35,24,34)(14,27,31,37,30,33,23,32);(2,3)(4,5)(6,7,12,17)(8,18,22,28)(9,23,25,31)(10,16,11,15)(13,20,29,21)(14,26,30,24)(19,33,35,27)(32,36,37,34)Polycyclic presentation:
2^6,5|a^2=f,b^2=ef,d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,g^a=g^4,d^c=df56 conjugacy classes — view the full character table.
| maximal subgroup of | #10599921, #10599922, #10601886, … |
| maximal normal subgroup of | #10599921, #10599922, #10601886, … |
| maximal quotient of | #10600684, #10600687, #10600697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 770);