Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ #102 |
50 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)(15,18)(16,21)(19,20);(2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15)(16,18)(17,20)(19,21)Polycyclic presentation:
2^5,13|a^2=c,d^2=e,b^a=bd,d^a=de,f^a=f^8,d^b=de,f^c=f^1229 conjugacy classes — view the full character table.
| maximal subgroup of | D8×#261, #11719102, SD16×#261, … |
| maximal normal subgroup of | D8×#261, #11719102, SD16×#261, … |
| maximal quotient of | #11718240, #11718243, #11718245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 82);