Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #364 |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8,9,16,11,17,15,20,12,18,14,21,10,19,7,13);(2,3)(4,5)(6,7,10,14,12,15,11,9)(8,16,17,20,18,21,19,13)Polycyclic presentation:
2^6,5|a^2=d,b^2=c,c^2=e,d^2=f,e^2=f,b^a=bd,g^a=g^4,d^b=df68 conjugacy classes — view the full character table.
| maximal subgroup of | #10599881, #10599882, #10599907, … |
| maximal normal subgroup of | #10599881, #10599882, #10599907, … |
| maximal quotient of | #10598045, #10598046, #10598301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 69);