Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #344 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8,10,17,11,18,9,16)(7,12,13,20,14,15,19,21);(2,3)(4,5)(6,7,9,13,11,14,10,19)(8,15,16,21,18,12,17,20)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=f,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 | #10599492, #10599507, #10599509, … |
| maximal normal subgroup of | #10599492, #10599507, #10599509, … |
| maximal quotient of | #10598153, #10598156, #10598159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 117);