Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C13 ⋊ C4 |
| 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:
(1,2,5,8,12,6,10,11,3,7,13,9,4)(14,16,17,21)(15,18,19,20);(2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15)(16,20,21,18)(17,19)Polycyclic presentation:
2^5,13|a^2=c,b^2=e,b^a=bd,d^a=de,f^a=f^8,c^b=ce,f^c=f^1235 conjugacy classes — view the full character table.
| maximal subgroup of | #11718225, #11718226, #11718294, … |
| maximal normal subgroup of | #11718225, #11718226, #11718294, … |
| maximal quotient of | #11718225, #11718226, #11718227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 74);