Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#108 ⋊ C2 |
| 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)(6,9,10,23,12,24,11,26)(7,14,15,21,16,32,25,31)(8,17,18,22,20,34,19,36)(13,27,28,33,29,37,35,30);(6,8,11,19,12,20,10,18)(7,13,15,28,16,29,25,35)(9,22,23,34,24,36,26,17)(14,30,31,37,32,33,21,27);(2,3)(4,5)(6,7)(8,13)(9,21)(10,25)(11,15)(12,16)(14,23)(17,33)(18,35)(19,28)(20,29)(22,27)(24,31)(26,32)(30,34)(36,37)Polycyclic presentation:
2^6,5|b^2=e,c^2=d,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10600037, #10600038, #10600052, … |
| maximal normal subgroup of | #10600037, #10600038, #10600052, … |
| maximal quotient of | #10599332, #10599334, #10599335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 523);