Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1300 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)(18,19,24,28,23,21,25,29)(20,26,33,41,32,35,34,30)(22,27,38,42,37,36,39,43)(31,40,46,44,45,48,47,49);(18,20,23,32)(19,26,21,35)(22,31,37,45)(24,34,25,33)(27,40,36,48)(28,30,29,41)(38,47,39,46)(42,49,43,44);(18,21)(19,23)(20,30)(22,36)(24,28)(25,29)(26,34)(27,37)(31,44)(32,41)(33,35)(38,42)(39,43)(40,46)(45,49)(47,48);(18,22)(19,27)(20,31)(21,36)(23,37)(24,39)(25,38)(26,40)(28,43)(29,42)(30,44)(32,45)(33,47)(34,46)(35,48)(41,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17410);