Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C11 ⋊ C2 |
| Sylow | C11 ⋊ #104 |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 88 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,4,6,8,10,11,9,7,5,3)(13,16,17,18);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,16)(15,17)(18,19)Polycyclic presentation:
2^5,11|b^2=c,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^1094 conjugacy classes — view the full character table.
| maximal subgroup of | #10622313, #10622330, D11×#104, … |
| maximal normal subgroup of | #10622313, #10622330, D11×#104, … |
| maximal quotient of | #10622089, #10622090, #10622094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 11);