Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #342 |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(10,12)(11,14)(13,17)(15,16);(2,3)(4,5)(10,11)(12,16,17,14)(13,15)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,b^a=be,e^a=ef,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10597939, #10597940, #10597941, … |
| maximal normal subgroup of | #10597939, #10597940, #10597941, … |
| maximal quotient of | #10598104, #10598107, #10598114, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 84);