Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#120 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
1060 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)(18,19,21,26,23,27,33,41)(20,25,29,39,31,40,44,49)(22,24,32,36,34,37,45,47)(28,38,42,48,30,35,43,46);(19,24)(21,32)(25,35)(27,37)(29,43)(33,45)(38,40)(42,44);(18,20,22,30)(19,25,24,35)(21,29,32,43)(23,31,34,28)(26,39,36,46)(27,40,37,38)(33,44,45,42)(41,49,47,48);(20,28)(25,38)(29,42)(30,31)(35,40)(39,48)(43,44)(46,49)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10410);