Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×Q16 ⋊ 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)(6,9,12,25)(7,14,16,31)(8,17,20,34)(10,24,11,23)(13,27,29,36)(15,32,26,21)(18,22,19,33)(28,37,35,30);(6,8,11,19,12,20,10,18)(7,13,15,28,16,29,26,35)(9,22,24,34,25,33,23,17)(14,30,21,36,31,37,32,27);(2,3)(4,5)(6,7)(8,13)(9,21)(10,26)(11,15)(12,16)(14,23)(17,30)(18,35)(19,28)(20,29)(22,36)(24,31)(25,32)(27,33)(34,37)Polycyclic presentation:
2^6,5|b^2=e,c^2=f,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,d^c=df,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10600063, #10600064, #10602283, … |
| maximal normal subgroup of | #10600063, #10600064, #10602283, … |
| maximal quotient of | #10601056, #10601057, #10601058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 819);