Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #102 |
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)(12,13,14,15)(17,20)(18,23)(21,22);(2,3)(4,5)(6,7)(8,9)(10,11)(16,17)(18,20)(19,22)(21,23)Polycyclic presentation:
2^5,11|b^2=c,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 | #10622373, #10622375, #10622377, … |
| maximal normal subgroup of | #10622373, #10622375, #10622377, … |
| maximal quotient of | #10622089, #10622120, #10622121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 15);