Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #356 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(7,11,14,13)(12,20,21,19);(2,3,4,5)(6,7,8,12,10,14,16,21)(9,13,17,20,18,11,15,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,c^2=f,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,c^b=ce,d^c=df,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | #10598520, #10598521, #10598542, … |
| maximal normal subgroup of | #10598520, #10598521, #10598542, … |
| maximal quotient of | #10598500, #10598502, #10598687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 193);