Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #484 |
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)(6,8,9,12)(7,11,10,13)(15,19)(16,21)(18,20);(7,10)(11,13)(15,18)(19,20);(2,3)(4,5)(6,7)(8,11)(9,10)(12,13)(14,15,17,18)(16,19,21,20)Polycyclic presentation:
2^6,5|a^2=f,c^2=ef,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,d^c=df59 conjugacy classes — view the full character table.
| maximal subgroup of | #10600508, #10600509, #10600510, … |
| maximal normal subgroup of | #10600508, #10600509, #10600510, … |
| maximal quotient of | #10600254, #10600258, #10600312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 597);