Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ #448 |
158 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)(10,11,13,15)(12,17,16,14);(7,9);(2,3)(4,5)(6,7)(8,9)(11,14)(12,16)(15,17)Polycyclic presentation:
2^6,5|c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,d^c=df59 conjugacy classes — view the full character table.
| maximal subgroup of | #10600492, #10600493, #10600498, … |
| maximal normal subgroup of | #10600492, #10600493, #10600498, … |
| maximal quotient of | #10602349, #10602353, #10602422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 854);