Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #349 |
58 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)(6,8,10,9,11,17,19,18)(7,12,15,20,14,16,21,13);(2,3,4,5)(6,7,9,13,10,15,17,12,11,14,18,20,19,21,8,16)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,c^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^2,c^b=cf,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598599, #10598600, #10598601, … |
| maximal normal subgroup of | #10598599, #10598600, #10598601, … |
| maximal quotient of | #10598580, #10598582, #10598760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 229);