Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11278 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #387 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1442 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
576 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)(20,30,32,45,33,25,39,41)(21,34,37,44,36,26,38,43)(31,40,48,49,47,46,35,42);(18,20)(19,25)(21,35,36,48)(22,32)(23,39)(24,33)(26,42,34,49)(27,30)(28,41)(29,45)(31,37,47,38)(40,43,46,44);(18,21)(19,26,27,34)(20,31)(22,38)(23,37)(24,36)(25,40,30,46)(28,44,29,43)(32,48)(33,47)(35,39)(41,49,45,42)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4266);