Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of #66890 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C11×Q16 ⋊ 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)(12,13,16,19)(14,21,23,27)(15,24,22,18)(17,25,26,20);(2,3)(4,5)(6,7)(8,9)(10,11)(13,17)(14,20)(15,22)(18,27)(19,26)(21,24)(23,25)Polycyclic presentation:
2^5,11|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^10,c^b=cd,d^b=de46 conjugacy classes — view the full character table.
| maximal subgroup of | D11×SD32, #10622527, #10622531, … |
| maximal normal subgroup of | D11×SD32, #10622527, #10622531, … |
| maximal quotient of | #10622128, #10622129, #10622202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 34);