Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #99 |
52 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)(14,16)(15,18)(17,21)(19,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,20,21,18)(17,19)Polycyclic presentation:
2^5,13|a^2=c,b^a=bd,d^a=de,f^a=f^12,c^b=ce71 conjugacy classes — view the full character table.
| maximal subgroup of | #11718065, #11718066, #11718067, … |
| maximal normal subgroup of | #11718065, #11718066, #11718067, … |
| maximal quotient of | #11718117, #11718118, #11718120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 41);