Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #478 |
102 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)(6,8,9,13)(7,10,11,12)(14,15,17,18)(16,21,20,19);(15,19)(16,20)(18,21);(2,3)(4,5)(6,7,9,11)(8,12,13,10)(15,18)(19,21)Polycyclic presentation:
2^6,5|a^2=d,c^2=df,e^2=f,c^a=cdf,g^a=g^4,c^b=ce,e^b=ef,e^c=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65055, #10610462, #10610490, … |
| maximal normal subgroup of | C2×#65055, #10610462, #10610490, … |
| maximal quotient of | #10599591, #10599595, #10599602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 393);