Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#1055 |
| Sylow | C13 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(15,17);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19,20,22,21,23,24,25)Polycyclic presentation:
2^5,13|a^2=c,c^2=e,b^a=bd,f^a=f^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #11718043, #11718044, #11718060, … |
| maximal normal subgroup of | #11718043, #11718044, #11718060, … |
| maximal quotient of | #11718116, #11718117, #11718120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 37);