Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#108 ⋊ C2 |
| Sylow | C5 ⋊ #361 |
62 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)(6,7,8,13,11,14,10,19)(9,17,15,12,18,20,16,21);(2,3)(4,5)(7,12)(8,10)(9,16)(13,17)(14,21)(15,18)(19,20)Polycyclic presentation:
2^6,5|b^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^4,d^b=def,e^b=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10600035, #10600037, D5×#361, … |
| maximal normal subgroup of | #10600035, #10600037, D5×#361, … |
| maximal quotient of | #10597956, #10597964, #10597967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 53);