Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #327 |
90 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)(7,10,11,12)(9,13)(14,15,19,21,17,20,16,18);(2,3)(4,5)(6,7)(8,12)(9,11)(10,13)(15,18)(16,19)(20,21)Polycyclic presentation:
2^6,5|b^2=cd,c^2=e,b^a=bc,c^a=ce,d^a=df,g^a=g^4,c^b=cf,d^b=df59 conjugacy classes — view the full character table.
| maximal subgroup of | #10598899, #10598900, #10598901, … |
| maximal normal subgroup of | #10598899, #10598900, #10598901, … |
| maximal quotient of | #10597939, #10597941, #10597947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 28);