Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #491 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,4,5,3)(7,11)(8,12)(14,16,18,24)(15,20,19,27)(17,25,26,23)(21,29,28,22);(6,8,9,12)(7,10,11,13)(15,19)(20,27)(21,28)(22,29);(2,3)(4,5)(6,7)(8,10)(9,11)(12,13)(14,15,17,21,18,19,26,28)(16,22,23,27,24,29,25,20)Polycyclic presentation:
2^6,5|a^2=e,b^2=d,c^2=f,e^2=f,b^a=bf,c^a=cde,g^a=g^4,c^b=cd,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10598042, #10598752, #10602039, … |
| maximal normal subgroup of | #10598042, #10598752, #10602039, … |
| maximal quotient of | #10600364, #10600368, #10600376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 709);