Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of #6095 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C13 ⋊ C2 |
| 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:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(15,18,19,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,18)(17,19)(20,21)Polycyclic presentation:
2^5,13|b^2=c,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #11718361, #11718378, D13×#104, … |
| maximal normal subgroup of | #11718361, #11718378, D13×#104, … |
| maximal quotient of | #11718043, #11718044, #11718048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 12);