Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #510 |
82 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)(7,13)(8,17)(9,20)(10,21)(12,24)(14,15)(16,30)(18,34)(22,31)(23,29)(25,36)(26,37)(27,28)(32,35);(6,8)(7,12)(9,18)(10,19)(11,17)(13,28)(14,25)(15,26)(16,27)(20,35)(21,33)(22,32)(23,36)(24,30)(29,37)(31,34);(2,3)(4,5)(6,7,11,16)(8,12,17,27)(9,13,22,30)(10,23,21,15)(14,31,29,20)(18,28,32,24)(19,36,33,26)(25,34,37,35)Polycyclic presentation:
2^6,5|a^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^4,c^b=cf,d^c=de,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10600037, #10600038, #10600041, … |
| maximal normal subgroup of | #10600037, #10600038, #10600041, … |
| maximal quotient of | #10601442, #10601447, #10601448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 822);