Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#97 ⋊ C2 |
| Sylow | C5 ⋊ #329 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,7,8,11,9,10,12,13)(15,18,19,20);(2,3)(4,5)(7,10)(8,12)(14,15)(16,18)(17,19)(20,21)Polycyclic presentation:
2^6,5|b^2=c,c^2=f,d^2=ef,b^a=bd,c^a=ce,d^a=def,g^a=g^4,d^b=df59 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#329, #10599135, #10599136, … |
| maximal normal subgroup of | D5×#329, #10599135, #10599136, … |
| maximal quotient of | #10597970, #10597971, #10598011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 22);