Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#10831 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #381 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1434 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
628 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)(20,28,30,24)(21,32)(22,27)(23,26)(25,33)(29,36,42,40)(31,41,44,37)(34,45)(35,39)(38,46)(43,47,49,48);(18,20,22,31,23,30,35,44)(19,24,27,37,26,28,39,41)(21,29,34,43,33,42,46,49)(25,36,38,47,32,40,45,48);(18,21)(19,25,26,32)(20,29)(22,34)(23,33)(24,36,28,40)(27,38,39,45)(30,42)(31,43)(35,46)(37,47,41,48)(44,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3819);