Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D13⋊M16 |
| Sylow | C13 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,5,8,12,6,10,11,3,7,13,9,4)(15,20)(19,21);(14,16,18,17)(15,19,20,21);(2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15,17,21,18,20,16,19)Polycyclic presentation:
2^5,13|a^2=d,b^2=e,d^2=e,c^a=ce,f^a=f^8,f^d=f^1244 conjugacy classes — view the full character table.
| maximal subgroup of | #11718234, #11718235, #11718266, … |
| maximal normal subgroup of | #11718234, #11718235, #11718266, … |
| maximal quotient of | #11719047, C4×#6118, #11719049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 201);