Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ #376 |
178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,3,5,4)(6,7,8,9)(11,15)(14,17);(10,12,13,16)(11,14,15,17);(2,3,4,5)(10,11)(12,14)(13,15)(16,17)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=e,c^a=cf,g^a=g^2,g^d=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10598526, #10598543, #10598584, … |
| maximal normal subgroup of | #10598526, #10598543, #10598584, … |
| maximal quotient of | #10603774, #10603800, #10603839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1024);