Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #107 |
36 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)(16,17,21,23,19,22,18,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14,15)(17,20)(18,21)(22,23)Polycyclic presentation:
2^5,11|a^2=c,b^2=de,d^2=e,b^a=bd,d^a=de,f^a=f^1094 conjugacy classes — view the full character table.
| maximal subgroup of | #10622127, #10622128, #10622141, … |
| maximal normal subgroup of | #10622127, #10622128, #10622141, … |
| maximal quotient of | #10622096, #10622142, #10622143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 24);