Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #343 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,5,4)(6,7,8,9)(11,14)(12,16);(2,3,4,5)(10,11,12,15,13,14,16,17)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=f,b^a=be,e^a=ef,g^a=g^2,c^b=cf,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598499, #10598500, #10598501, … |
| maximal normal subgroup of | #10598499, #10598500, #10598501, … |
| maximal quotient of | #10598697, #10598707, #10598722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 257);