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:
(1,2,4,5,3)(10,11,12,15,13,14,16,17);(2,3)(4,5)(6,7,8,9)(11,14)(12,16)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,d^2=f,b^a=be,d^a=df,g^a=g^4,e^b=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599528, #10599529, #10599556, … |
| maximal normal subgroup of | #10599528, #10599529, #10599556, … |
| maximal quotient of | #10598150, #10598159, #10598160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 112);