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)(7,11,13,14)(9,15)(10,16)(12,19,20,21)(17,18);(2,3)(4,5)(6,7,9,12,10,13,17,20)(8,14,15,21,16,11,18,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^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 | #10599489, #10599492, #10599493, … |
| maximal normal subgroup of | #10599489, #10599492, #10599493, … |
| maximal quotient of | #10598106, #10598108, #10598111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 91);