Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #442 |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(11,14)(12,16)(15,17);(10,12)(11,15)(13,17)(14,16);(2,3)(4,5)(6,7,8,9)(10,11,13,14)(12,15,17,16)Polycyclic presentation:
2^6,5|a^2=d,e^2=f,c^a=cf,g^a=g^4,c^b=ce,e^b=ef,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #10600047, #10602308, #10611307, … |
| maximal normal subgroup of | #10600047, #10602308, #10611307, … |
| maximal quotient of | #10600945, #10600949, #10600963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 779);