Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#168 |
| Sylow | C5 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(14,15,17,19)(16,21,20,18);(2,3)(4,5)(6,7,8,10,9,11,12,13)(15,18)(16,20)(19,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^4,d^b=df68 conjugacy classes — view the full character table.
| maximal subgroup of | D5×Q8⋊C8, #10599022, #10599023, … |
| maximal normal subgroup of | D5×Q8⋊C8, #10599022, #10599023, … |
| maximal quotient of | #10598110, #10598129, #10598133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 93);