Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #361 |
62 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)(8,16)(9,19)(12,13)(14,21)(15,18)(17,20);(2,3,4,5)(6,7,8,12,10,15,16,14)(9,18,17,13,20,11,19,21)Polycyclic presentation:
2^6,5|a^2=c,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,c^b=cf,d^b=def,e^b=ef,g^c=g^423 conjugacy classes — view the full character table.
| maximal subgroup of | #10604124, #10604125, #10604132, … |
| maximal normal subgroup of | #10604124, #10604125, #10604132, … |
| maximal quotient of | #10598607, #10598613, #10598618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 244);