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×#33842 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3283 | 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)(22,23,28,25)(24,32,35,51)(26,39,43,50)(27,38,41,31)(29,46,36,34)(30,45,37,42)(33,52,44,48)(40,49,53,47);(22,24,28,35)(23,29,25,36)(26,40,43,53)(27,44,41,33)(30,48,37,52)(31,49,38,47)(32,50,51,39)(34,45,46,42);(19,21)(22,25,28,23)(24,29,35,36)(26,37,43,30)(27,38,41,31)(32,46,51,34)(33,47,44,49)(39,42,50,45)(40,48,53,52);(22,26)(23,30)(24,33)(25,37)(27,45)(28,43)(29,47)(31,50)(32,51)(34,46)(35,44)(36,49)(38,39)(41,42)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26830);