Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3958 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #368 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,4,5,3)(6,8,9,17,11,20,22,19)(7,12,13,25,15,27,29,26)(10,23,21,18,24,34,36,35)(14,30,28,16,31,32,37,33);(2,3)(4,5)(6,7,10,14,22,29,36,37,11,15,24,31,9,13,21,28)(8,16,18,25,17,32,34,27,20,33,35,26,19,30,23,12)Polycyclic presentation:
2^6,5|a^2=d,b^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,g^a=g^4,d^b=de,e^b=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #10600031, #10600032, #10600053, … |
| maximal normal subgroup of | #10600031, #10600032, #10600053, … |
| maximal quotient of | #10597960, #10597961, #10598219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 51);