Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#20860 |
| 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 | |
1296 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)(18,19,23,28,24,27,22,35)(20,29,31,25,32,40,36,39)(21,26,33,43,34,41,37,42)(30,45,48,49,47,44,46,38);(18,20,23,31,24,32,22,36)(19,25,28,40,27,39,35,29)(21,30,33,48,34,47,37,46)(26,38,43,45,41,49,42,44);(18,21)(19,26)(20,30)(22,37)(23,33)(24,34)(25,38)(27,41)(28,43)(29,44)(31,48)(32,47)(35,42)(36,46)(39,49)(40,45);(19,27)(25,39)(26,41)(28,35)(29,40)(38,49)(42,43)(44,45)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13848);