Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
398 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)(18,19)(20,21)(22,23,28,34)(24,35,39,46)(25,29,26,42)(27,44,41,33)(30,36,48,37)(31,43,32,40)(38,45,51,49)(47,53,50,52);(23,29)(24,36)(25,40)(26,43)(27,41)(31,33)(32,44)(34,42)(35,49)(37,39)(38,53)(45,46)(47,50)(51,52);(19,21)(22,24,25,36,41,51,43,53,28,39,26,37,27,38,40,52)(23,30,31,46,44,50,42,49,34,48,32,35,33,47,29,45)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6428);