Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#101 ⋊ C2 |
| Sylow | C5 ⋊ #355 |
64 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)(6,7,8,12,10,13,15,21)(9,11,17,18,16,19,14,20);(2,3)(4,5)(7,11)(9,16)(12,20)(13,19)(14,17)(18,21)Polycyclic presentation:
2^6,5|b^2=c,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^4,d^b=def,e^b=ef,d^c=df35 conjugacy classes — view the full character table.
| maximal subgroup of | #10599953, #10599954, D5×#355, … |
| maximal normal subgroup of | #10599953, #10599954, D5×#355, … |
| maximal quotient of | #10597943, #10597945, #10597947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 35);