Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#108 ⋊ C2 |
| Sylow | C5 ⋊ #430 |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,8,9,17,11,18,10,19)(7,13,14,16,12,20,15,21);(6,7,10,15,11,12,9,14)(8,16,17,20,18,21,19,13);(2,3)(4,5)(7,12)(13,20)(14,15)(16,21)Polycyclic presentation:
2^6,5|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bf,g^a=g^4,c^b=ce,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #10600050, #10600060, #10600106, … |
| maximal normal subgroup of | #10600050, #10600060, #10600106, … |
| maximal quotient of | #10599321, #10599324, #10599325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 520);