Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of D176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C11×C16 ⋊ C2 |
| Sylow | C11 ⋊ SD32 |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,8,10,11,9,7,5,3)(12,13,18,24,23,27,14,17,16,20,21,26,15,19,22,25);(2,3)(4,5)(6,7)(8,9)(10,11)(13,17)(14,21)(15,23)(18,22)(19,26)(20,25)(24,27)Polycyclic presentation:
2^5,11|b^2=cd,c^2=d,d^2=e,b^a=bc,c^a=cde,d^a=de,f^a=f^1091 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#66864, #10622517, #10622521, … |
| maximal normal subgroup of | C2×#66864, #10622517, #10622521, … |
| maximal quotient of | #10622141, #10622143, #10622147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 6);