Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #441 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(6,7,8,9)(12,20)(15,24)(18,25)(21,23);(10,12,19,23,14,20,13,21)(11,15,22,25,17,24,16,18);(2,3)(4,5)(10,11,14,17)(12,18,20,25)(13,22,19,16)(15,23,24,21)Polycyclic presentation:
2^6,5|a^2=f,b^2=ef,c^2=d,e^2=f,b^a=be,e^a=ef,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599883, #10601721, #10610225, … |
| maximal normal subgroup of | #10599883, #10601721, #10610225, … |
| maximal quotient of | #10598877, #10598880, #10598882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 343);