Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13309 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13466 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #2065 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
314 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)(18,19,26,31)(20,32)(21,38)(22,29,43,49)(23,28,24,46)(25,33,45,30)(27,40)(34,42)(35,48)(36,39)(37,47)(41,44);(18,20,22,34,25,36,23,44,26,37,43,38,45,27,24,35)(19,21,28,32,30,41,29,40,31,42,46,47,33,48,49,39);(18,21)(19,27)(20,33)(22,40)(23,32)(24,47)(25,48)(26,42)(28,34)(29,35)(30,37)(31,36)(38,46)(39,43)(41,45)(44,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6454);