Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
980 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)(22,23,28,32,29,34,27,33)(24,35,37,30,25,39,38,46)(26,41,42,31,44,48,43,49)(36,45,52,53,40,47,51,50);(18,19)(20,21)(22,24,28,37,29,25,27,38)(23,30,32,39,34,46,33,35)(26,40,42,51,44,36,43,52)(31,47,48,50,49,45,41,53);(19,21)(22,25,29,24)(23,30,34,46)(26,40,44,36)(27,38,28,37)(31,45,49,47)(32,35,33,39)(41,53,48,50)(42,52,43,51);(22,26)(23,31)(24,36)(25,40)(27,43)(28,42)(29,44)(30,45)(32,48)(33,41)(34,49)(35,50)(37,52)(38,51)(39,53)(46,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18182);