Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #362 |
54 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)(6,8,9,17,11,20,23,19)(7,12,13,28,15,30,21,29)(10,25,22,27,26,36,31,18)(14,32,24,35,33,34,37,16);(2,3)(4,5)(6,7,11,15)(8,16,20,35)(9,21,23,13)(10,24,26,37)(12,27,30,18)(14,31,33,22)(17,34,19,32)(25,29,36,28)Polycyclic presentation:
2^6,5|a^2=f,b^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^4,d^b=def,e^b=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10600036, #10600038, #10600049, … |
| maximal normal subgroup of | #10600036, #10600038, #10600049, … |
| maximal quotient of | #10597957, #10597965, #10597966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 54);