Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #419 |
150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(10,13,15,22)(11,17,18,25)(12,19,14,21)(16,24,23,20);(10,12,15,14)(11,16,18,23)(13,21,22,19)(17,20,25,24);(2,3)(4,5)(6,7,8,9)(10,11)(12,16)(13,20)(14,23)(15,18)(17,19)(21,25)(22,24)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^4,c^b=cf,e^c=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | #10600466, #10600486, #10600899, … |
| maximal normal subgroup of | #10600466, #10600486, #10600899, … |
| maximal quotient of | #10602346, #10602351, #10602414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 852);