Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3993 |
| 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:
(1,2,3,5,4)(6,7,8,9)(10,12,13,20,15,22,14,21)(11,16,23,25,18,24,17,19);(2,3,4,5)(10,11,13,17,15,18,14,23)(12,19,20,24,22,25,21,16)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^2,g^c=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598613, #10598614, #10598806, … |
| maximal normal subgroup of | #10598613, #10598614, #10598806, … |
| maximal quotient of | #10598531, #10598532, #10598557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 234);