Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×D8 ⋊ C4 |
| Sylow | C5 ⋊ #442 |
132 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)(7,10)(8,12)(11,13);(6,8)(7,11)(9,13)(10,12);(2,3,4,5)(6,7,9,10)(8,11,13,12)Polycyclic presentation:
2^6,5|a^2=d,e^2=f,c^a=cf,g^a=g^2,c^b=ce,e^b=ef,e^c=ef,g^d=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | #10604124, #10604125, #10604132, … |
| maximal normal subgroup of | #10604124, #10604125, #10604132, … |
| maximal quotient of | #10603938, #10603944, #10603945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1069);