Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#29441 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C17×#376 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(34,35,39,41,38,43,37,42)(36,40,46,49,44,48,45,47);(18,20,21,25)(19,22,23,24)(26,27)(28,31)(29,30)(32,33)(34,36)(35,40)(37,45)(38,44)(39,46)(41,49)(42,47)(43,48);(27,30)(31,33)(35,41)(36,44)(37,39)(40,47)(42,43)(48,49);(19,23)(22,24)(26,28,29,32)(27,31,30,33)(36,44)(40,48)(45,46)(47,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 22429);