Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25443 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25445 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3060 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
886 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)(22,23,26,29,28,33,27,32)(24,34,35,30,38,45,37,46)(25,39,41,31,40,43,42,47)(36,44,49,52,51,53,50,48);(18,19)(20,21)(23,29,33,32)(24,35,38,37)(25,40)(31,39,47,43)(36,50,51,49)(41,42)(44,53)(48,52);(19,21)(22,24)(23,30)(25,36)(26,37)(27,35)(28,38)(29,34)(31,44)(32,45)(33,46)(39,52)(40,51)(41,50)(42,49)(43,48)(47,53);(22,25,27,42,28,40,26,41)(23,31,29,43,33,47,32,39)(24,36,35,49,38,51,37,50)(30,44,34,48,46,53,45,52)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18433);