Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| 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)(15,18)(16,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,19,17,18,20,21)Polycyclic presentation:
2^5,13|a^2=c,c^2=e,b^a=bd,d^a=de,f^a=f^12,c^b=ce71 conjugacy classes — view the full character table.
| maximal subgroup of | #11718063, #11718064, #11718128, … |
| maximal normal subgroup of | #11718063, #11718064, #11718128, … |
| maximal quotient of | #11718117, #11718122, #11718132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 40);