Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64868 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #330 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(6,7,9,11)(8,12,13,10)(14,16)(15,18)(17,20)(19,21);(2,3,4,5)(7,10,11,12)(14,15,17,19,18,16,21,20)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,c^2=ef,d^2=f,b^a=bd,d^a=def,g^a=g^2,c^b=ce,d^b=df,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#64870, #10604265, #10604266, … |
| maximal normal subgroup of | C2×#64870, #10604265, #10604266, … |
| maximal quotient of | #10598713, #10598714, #10598722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 208);