Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×M32 ⋊ C2 |
| Sylow | C5 ⋊ #360 |
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:
(1,2,4,5,3)(6,8,16,7,11,18,9,13,12,19,15,14,10,21,20,17);(2,3)(4,5)(6,7)(8,15)(9,18)(10,13)(11,17)(12,14)(16,19)(20,21)Polycyclic presentation:
2^6,5|b^2=cd,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^4,c^b=cf,d^b=df56 conjugacy classes — view the full character table.
| maximal subgroup of | #10599883, #10599884, #10599913, … |
| maximal normal subgroup of | #10599883, #10599884, #10599913, … |
| maximal quotient of | #10598007, #10598008, #10598017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 76);