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×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #331 |
84 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)(16,21)(19,20);(2,3)(4,5)(7,10)(8,12)(14,15)(16,18)(17,20)(19,21)Polycyclic presentation:
2^6,5|b^2=c,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^4,d^b=def59 conjugacy classes — view the full character table.
| maximal subgroup of | #10598975, #10598979, #10598981, … |
| maximal normal subgroup of | #10598975, #10598979, #10598981, … |
| maximal quotient of | #10597958, #10597964, #10597965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 43);