Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×Q16 ⋊ C4 |
| Sylow | C5 ⋊ #443 |
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,5,4)(6,9,11,19)(7,12,14,15)(8,13,16,21)(10,17,20,18);(6,8,11,16)(7,9,14,19)(10,12,20,15)(13,17,21,18);(2,3,4,5)(6,7,10,13,11,14,20,21)(8,9,12,17,16,19,15,18)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=f,d^2=f,e^2=f,g^a=g^2,c^b=ce,e^b=ef,e^c=ef,g^d=g^435 conjugacy classes — view the full character table.
| maximal subgroup of | #10604128, #10604129, #10604136, … |
| maximal normal subgroup of | #10604128, #10604129, #10604136, … |
| maximal quotient of | #10603967, #10603975, #10603978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1078);