Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24293 |
| 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 | |
1290 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)(24,30)(25,38)(26,41)(27,34)(28,33)(29,36)(31,42)(32,39)(35,50)(37,45)(40,44)(43,49)(46,51)(47,52)(48,53);(22,24,27,36,28,25,39,37)(23,29,32,30,33,45,34,38)(26,35,42,51,43,40,53,52)(31,44,41,46,48,50,49,47);(19,21)(22,25)(23,30)(24,28)(26,35)(27,37)(29,34)(31,47)(32,45)(33,38)(36,39)(40,43)(41,44)(42,51)(46,48)(49,50)(52,53);(22,26,39,53,28,43,27,42)(23,31,34,49,33,48,32,41)(24,35,37,52,25,40,36,51)(29,44,38,47,45,50,30,46)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17281);