Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ #428 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2,3,5,4)(6,7,8,10,9,11,12,13);(7,11)(10,13);(2,3,4,5)(7,10)(8,12)(11,13)Polycyclic presentation:
2^6,5|a^2=d,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^2,c^b=cf,g^d=g^432 conjugacy classes — view the full character table.
| maximal subgroup of | #10603925, #10603927, #10603931, … |
| maximal normal subgroup of | #10603925, #10603927, #10603931, … |
| maximal quotient of | #10603865, #10603866, #10603867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1065);