Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ #418 |
190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(10,11,12,14,13,15,16,17);(11,15)(14,17);(2,3)(4,5)(11,14)(12,16)(15,17)Polycyclic presentation:
2^6,5|c^2=de,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599506, #10599519, #10599553, … |
| maximal normal subgroup of | #10599506, #10599519, #10599553, … |
| maximal quotient of | #10600605, #10600616, #10600621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 758);