Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11280 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #393 |
| commutator | C24 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1442 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
580 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)(18,19,22,27,23,26,37,43)(20,28,31,44,30,24,36,39)(21,32,35,46,34,25,40,42)(29,38,45,48,33,41,47,49);(18,20)(19,24)(21,33,34,29)(22,36)(23,30)(25,41,32,38)(26,28)(27,44)(31,37)(35,45,40,47)(39,43)(42,48,46,49);(18,21)(19,25,26,32)(20,29)(22,35)(23,34)(24,38,28,41)(27,42,43,46)(30,33)(31,45)(36,47)(37,40)(39,48,44,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4268);