Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3993 |
| 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:
(1,2,3,5,4)(6,8,10,18,12,19,11,9)(7,13,15,17,16,14,20,21);(2,3,4,5)(6,7,9,14,11,15,19,21,12,16,18,13,10,20,8,17)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^2,g^c=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598623, #10598624, #10598648, … |
| maximal normal subgroup of | #10598623, #10598624, #10598648, … |
| maximal quotient of | #10598522, #10598524, #10598779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 227);