Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3993 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ #339 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,3,5,4)(7,10,11,12);(2,3,4,5)(6,7)(8,10)(9,11)(12,13)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,e^2=f,b^a=be,d^a=df,e^a=ef,g^a=g^2,g^c=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10603851, #10603853, #10603885, … |
| maximal normal subgroup of | #10603851, #10603853, #10603885, … |
| maximal quotient of | #10598504, #10598507, #10598509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 200);