Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #341 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,5,3)(10,12,13,21,15,22,14,23)(11,16,17,24,19,25,18,20);(2,3)(4,5)(6,7,8,9)(10,11,14,18,15,19,13,17)(12,20,21,16,22,24,23,25)Polycyclic presentation:
2^6,5|a^2=d,b^2=c,c^2=f,d^2=f,b^a=bde,g^a=g^4,d^b=df68 conjugacy classes — view the full character table.
| maximal subgroup of | #10599493, #10599511, #10599531, … |
| maximal normal subgroup of | #10599493, #10599511, #10599531, … |
| maximal quotient of | #10598153, #10598158, #10598160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 116);