Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #498 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,8,9,13)(7,10,11,12)(15,18)(16,20)(19,21);(6,7,9,11)(8,12,13,10);(2,3)(4,5)(14,15,16,18,17,19,20,21)Polycyclic presentation:
2^6,5|a^2=e,b^2=d,c^2=d,e^2=f,c^a=cef,g^a=g^4,c^b=cd,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #10599231, #10599232, #10599235, … |
| maximal normal subgroup of | #10599231, #10599232, #10599235, … |
| maximal quotient of | #10600363, #10600369, #10600375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 706);