Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C11 ⋊ 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)(16,17,18,20,19,21,22,23);(2,3)(4,5)(6,7)(8,9)(10,11)(17,20)(18,22)(21,23)Polycyclic presentation:
2^5,11|b^2=cd,c^2=e,b^a=bc,c^a=ce,f^a=f^1094 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4314, C4×D88, #10622307, … |
| maximal normal subgroup of | C4×#4314, C4×D88, #10622307, … |
| maximal quotient of | #10622097, #10622108, #10622123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 27);