Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#1057 |
| Sylow | C13 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,5,8,12,6,10,11,3,7,13,9,4)(14,15,16,17);(2,3,4,6)(5,8,9,13)(7,11,12,10)(15,17)(18,19,20,22,21,23,24,25)Polycyclic presentation:
2^5,13|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^8,f^c=f^1244 conjugacy classes — view the full character table.
| maximal subgroup of | #11718243, #11718244, #11718253, … |
| maximal normal subgroup of | #11718243, #11718244, #11718253, … |
| maximal quotient of | C4⋊#6092, #11718253, #11718254, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 76);