Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #103 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,8,10,11,9,7,5,3)(16,17,19,21)(18,23,22,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14,15)(17,20)(18,22)(21,23)Polycyclic presentation:
2^5,11|a^2=c,b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^10,d^b=de64 conjugacy classes — view the full character table.
| maximal subgroup of | #10622404, #10622405, #10622407, … |
| maximal normal subgroup of | #10622404, #10622405, #10622407, … |
| maximal quotient of | #10622167, Q8⋊(C11⋊C8), #10622176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 41);