Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D11)⋊C8 |
| Fitting | C2×C8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,8,10,11,9,7,5,3)(13,15)(16,17,18,20,19,21,22,23);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)Polycyclic presentation:
2^5,11|b^2=c,c^2=e,b^a=bd,f^a=f^10100 conjugacy classes — view the full character table.
| maximal subgroup of | #10622298, C8×D44, #10622301, … |
| maximal normal subgroup of | #10622298, C8×D44, #10622301, … |
| maximal quotient of | #10622094, #10622097, #10622106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 26);