Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#20867 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×#120 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#385 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1312 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)(18,19,23,28,24,27,22,38)(20,29,31,25,33,41,32,40)(21,34,36,26,37,43,35,42)(30,45,46,44,47,39,48,49);(18,20,23,31,24,33,22,32)(19,25,28,41,27,40,38,29)(21,30,36,46,37,47,35,48)(26,39,43,49,42,45,34,44);(18,21)(19,26)(20,30)(22,35)(23,36)(24,37)(25,39)(27,42)(28,43)(29,44)(31,46)(32,48)(33,47)(34,38)(40,45)(41,49);(19,27)(25,40)(26,42)(28,38)(29,41)(34,43)(39,45)(44,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13855);