Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #324 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(14,16,17,21)(15,18,19,20);(2,3,4,5)(6,7,8,10,9,11,12,13)(14,15)(16,20,21,18)(17,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,c^2=e,b^a=bd,d^a=df,g^a=g^2,c^b=cf,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598686, #10598687, #10598688, … |
| maximal normal subgroup of | #10598686, #10598687, #10598688, … |
| maximal quotient of | #10598688, #10598689, #10598690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 251);