Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #428 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(6,8,9,7)(10,11)(12,17)(13,15)(14,16);(11,15)(14,17);(2,3)(4,5)(6,7,9,8)(11,14)(12,16)(15,17)Polycyclic presentation:
2^6,5|a^2=e,c^2=e,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=cf,d^c=df62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599526, #10599527, #10599528, … |
| maximal normal subgroup of | #10599526, #10599527, #10599528, … |
| maximal quotient of | #10600259, #10600260, #10600274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 622);