Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#577 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
1328 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 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)(24,29)(25,37)(26,28)(27,32)(30,38)(31,41)(33,44)(34,49)(35,42)(36,45)(39,46)(40,47)(43,48)(50,52)(51,53);(23,28)(24,33)(26,41)(30,37)(31,32)(34,48)(35,36)(38,39)(42,44)(46,47)(49,52)(50,51);(19,21)(22,24,27,36)(23,29,32,45)(25,34,40,50)(26,35,41,33)(28,42,31,44)(30,43,46,53)(37,49,47,52)(38,48,39,51);(22,25)(23,30)(24,34)(26,39)(27,40)(28,37)(29,43)(31,47)(32,46)(33,48)(35,51)(36,50)(38,41)(42,49)(44,52)(45,53)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17446);