Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #423 |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(7,9)(10,11,12,15,13,14,16,17);(11,14)(15,17);(2,3)(4,5)(6,7,8,9)Polycyclic presentation:
2^6,5|a^2=e,c^2=d,d^2=f,c^a=ce,g^a=g^4,c^b=cf68 conjugacy classes — view the full character table.
| maximal subgroup of | #10598023, #10598784, #10598788, … |
| maximal normal subgroup of | #10598023, #10598784, #10598788, … |
| maximal quotient of | #10600602, #10600629, #10600701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 745);