Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11302 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #397 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1443 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,29,24,27,22,28)(20,25,33,42,31,41,32,40)(21,34,36,43,37,44,38,26)(30,45,46,49,35,48,47,39);(18,20,22,33,24,31,23,32)(19,25,29,40,27,41,28,42)(21,35,36,46,37,30,38,47)(26,39,44,45,43,49,34,48);(18,21)(19,26,27,43)(20,30,31,35)(22,36)(23,38)(24,37)(25,39)(28,34,29,44)(32,46,33,47)(40,45)(41,49)(42,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4290);