Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #117 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,8,10,11,9,7,5,3)(12,13,14,15)(18,22)(20,23);(16,18)(17,20)(19,22)(21,23);(2,3)(4,5)(6,7)(8,9)(10,11)(16,17,19,21)(18,20,22,23)Polycyclic presentation:
2^5,11|a^2=e,c^2=d,f^a=f^10,c^b=ce70 conjugacy classes — view the full character table.
| maximal subgroup of | #10622353, C2×#66930, #10623017, … |
| maximal normal subgroup of | #10622353, C2×#66930, #10623017, … |
| maximal quotient of | #10622261, #10622262, #10622263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 72);