Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#29437 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C17×#376 ◁ G | |
708 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)(34,35,37,41,38,42,45,40)(36,39,44,46,43,47,49,48);(18,20,21,25)(19,22,23,24)(26,27)(28,31)(29,30)(32,33)(34,36)(35,39)(37,44)(38,43)(40,48)(41,46)(42,47)(45,49);(27,30)(31,33)(35,40)(36,43)(37,45)(39,46)(41,42)(47,48);(19,23)(22,24)(26,28,29,32)(27,31,30,33)(36,43)(39,47)(44,49)(46,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 22425);