Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #104 |
44 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)(14,16,19,15)(17,21,18,20);(2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15,17,20,19,16,18,21)Polycyclic presentation:
2^5,13|a^2=c,b^2=e,c^2=e,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 | #11719107, #11719108, #11719111, … |
| maximal normal subgroup of | #11719107, #11719108, #11719111, … |
| maximal quotient of | #11718240, #11718242, #11718243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 85);