Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#10955 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1437 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
900 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,29,24,27,23,28)(20,25,32,40,31,41,37,39)(21,33,35,26,34,42,36,43)(30,44,45,38,46,47,48,49);(18,20,23,32,24,31,22,37)(19,25,29,39,27,41,28,40)(21,30,36,45,34,46,35,48)(26,38,42,44,43,49,33,47);(18,21,24,34)(19,26)(20,30,31,46)(22,35,23,36)(25,38)(27,43)(28,33)(29,42)(32,45,37,48)(39,44)(40,47)(41,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3943);