Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| 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);(7,12)(13,20)(14,15)(16,21);(2,3)(4,5)(6,7,10,15,11,12,9,14)(8,16,17,20,18,21,19,13)Polycyclic presentation:
2^6,5|a^2=e,c^2=d,d^2=f,e^2=f,b^a=bf,c^a=ce,g^a=g^4,e^c=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599499, #10599502, #10599515, … |
| maximal normal subgroup of | #10599499, #10599502, #10599515, … |
| maximal quotient of | #10600666, #10600668, #10600776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 751);