Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #480 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(7,11)(8,13)(14,15,19,21,17,20,16,18);(6,8)(7,10)(9,13)(11,12);(2,3)(4,5)(6,7)(8,12)(9,11)(10,13)(15,18)(16,19)(20,21)Polycyclic presentation:
2^6,5|c^2=def,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=ce59 conjugacy classes — view the full character table.
| maximal subgroup of | #10598903, #10598904, #10598927, … |
| maximal normal subgroup of | #10598903, #10598904, #10598927, … |
| maximal quotient of | #10599414, #10599418, #10599428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 363);