Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×C22⋊C4 ⋊ C2 |
| 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)(15,18,19,20)(17,21);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,20)(17,19)(18,21)Polycyclic presentation:
2^5,13|b^2=c,b^a=bd,c^a=ce,f^a=f^12,d^b=de71 conjugacy classes — view the full character table.
| maximal subgroup of | #11718401, #11718402, #11718403, … |
| maximal normal subgroup of | #11718401, #11718402, #11718403, … |
| maximal quotient of | #11718043, #11718044, #11718059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 13);