Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #99 |
52 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)(12,14)(13,16)(15,19)(17,18);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,18,19,16)(15,17)Polycyclic presentation:
2^5,11|a^2=c,b^a=bd,d^a=de,f^a=f^10,c^b=ce61 conjugacy classes — view the full character table.
| maximal subgroup of | #10622111, #10622112, #10622113, … |
| maximal normal subgroup of | #10622111, #10622112, #10622113, … |
| maximal quotient of | #10622163, #10622164, #10622166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 40);