Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D5⋊#131 |
| Sylow | C5 ⋊ C2×#131 |
266 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2,3,5,4)(8,17)(12,20)(16,18)(19,21);(6,9,11,10)(7,13,15,14)(8,16,17,18)(12,19,20,21);(6,8)(7,12)(9,16)(10,18)(11,17)(13,19)(14,21)(15,20);(2,3,4,5)(6,7,10,14,11,15,9,13)(8,12,18,21,17,20,16,19)Polycyclic presentation:
2^6,5|a^2=e,c^2=f,e^2=f,g^a=g^2,d^b=df,g^e=g^450 conjugacy classes — view the full character table.
| maximal subgroup of | #10604005, #10604006, #10604866, … |
| maximal normal subgroup of | #10604005, #10604006, #10604866, … |
| maximal quotient of | #10617105, D5⋊#424, D5⋊#433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1601);