Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C13×M16 ⋊ C2 |
| Sylow | C13 ⋊ #100 |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,16,19,17,18,20,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,18)(16,20)Polycyclic presentation:
2^5,13|b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^12,d^b=de71 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#100, #11718410, #11718412, … |
| maximal normal subgroup of | D13×#100, #11718410, #11718412, … |
| maximal quotient of | #11718056, #11718060, #11718073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 30);