Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #475 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,8,9,13)(7,10,11,12)(15,18)(16,21)(19,20);(14,15,17,20)(16,18,21,19);(2,3)(4,5)(6,7,9,11)(8,12,13,10)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=d,e^2=f,c^a=cd,g^a=g^4,c^b=ce,e^b=ef,e^c=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65080, #10610510, #10610536, … |
| maximal normal subgroup of | C2×#65080, #10610510, #10610536, … |
| maximal quotient of | #10599589, #10599593, #10599602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 418);