Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13068 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1893 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
470 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)(20,29)(21,34,37,45)(22,32)(23,27)(24,31)(25,28)(26,36,44,42)(30,35,43,38)(33,39)(40,41)(46,47,49,48);(18,20,29,19,24,32,40,27,25,33,39,28,23,41,22,31)(21,30,46,26,36,48,35,45,37,43,49,44,42,47,38,34);(18,21)(19,26)(20,30)(22,38)(23,42)(24,36)(25,37)(27,45)(28,44)(29,46)(31,34)(32,48)(33,43)(35,40)(39,49)(41,47)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6056);