Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33836 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3285 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(23,28)(24,32)(25,36)(26,39)(29,46)(30,50)(31,45)(33,49)(34,47)(35,42)(37,41)(40,43)(44,48)(51,52);(22,23,27,31)(24,33,35,46)(25,37,40,50)(26,41,39,30)(28,43,45,36)(29,47,49,34)(32,52,42,44)(38,51,53,48);(19,21);(22,24,27,35)(23,29,31,49)(25,38,40,53)(26,42,39,32)(28,44,45,52)(30,51,41,48)(33,50,46,37)(34,43,47,36)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26824);