Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #341 |
90 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)(6,8,9,16,11,17,10,19)(7,12,13,20,14,21,18,15);(2,3,4,5)(6,7,9,13,11,14,10,18)(8,15,16,12,17,20,19,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=f,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^2,e^b=ef,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10603927, #10603928, #10603933, … |
| maximal normal subgroup of | #10603927, #10603928, #10603933, … |
| maximal quotient of | #10598547, #10598548, #10598549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 239);