Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #483 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(8,12)(10,13)(14,15,17,19)(16,21,20,18);(6,8)(7,10)(9,12)(11,13);(2,3)(4,5)(6,7,9,11)(8,10,12,13)(15,18)(16,20)(19,21)Polycyclic presentation:
2^6,5|a^2=e,c^2=f,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10599113, #10599114, #10599121, … |
| maximal normal subgroup of | #10599113, #10599114, #10599121, … |
| maximal quotient of | #10600294, #10600298, #10600300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 670);