Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18138 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C25×C17 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1054 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,23,27)(20,28,30,44)(21,32,34,46)(22,25,36,40)(24,37,39,29)(26,41,43,35)(31,42,45,49)(33,38,47,48);(18,20,22,31)(19,24,25,38)(21,33,35,29)(23,30,36,45)(26,42,32,28)(27,39,40,48)(34,47,41,37)(43,49,46,44);(21,34)(26,43)(28,44)(29,37)(32,46)(33,47)(35,41)(42,49);(19,25)(24,38)(26,32)(27,40)(28,42)(39,48)(43,46)(44,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11126);