Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13338 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3155 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,28,34)(24,35,38,47)(25,29,26,42)(27,45,41,33)(30,48,51,37)(31,43,32,39)(36,49,46,52)(40,50,44,53);(18,19)(20,21)(23,29)(24,36)(25,39)(26,43)(27,41)(30,49)(31,33)(32,45)(34,42)(35,53)(37,48)(38,46)(47,50)(51,52);(19,21)(22,24)(23,30)(25,40)(26,44)(27,46)(28,38)(29,47)(31,49)(32,52)(33,53)(34,51)(35,42)(36,41)(37,43)(39,48)(45,50)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6326);