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×#24461 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
1318 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)(24,33)(25,39)(26,42)(27,31)(28,32)(29,36)(30,40)(34,38)(35,44)(37,45)(41,46)(43,47)(48,50)(49,52)(51,53);(22,24,28,38)(23,29,32,45)(25,35,41,51)(26,37,27,36)(30,44,47,53)(31,34,42,33)(39,48,46,49)(40,52,43,50);(19,21)(22,23)(24,34)(25,30)(26,31)(27,42)(28,32)(29,36)(33,38)(35,49)(37,45)(39,40)(41,47)(43,46)(44,52)(48,51)(50,53);(22,25,28,41)(23,30,32,47)(24,35,38,51)(26,43,27,40)(29,44,45,53)(31,46,42,39)(33,48,34,49)(36,52,37,50)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17449);