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×#33844 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
674 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)(22,23,28,32)(24,33,34,52)(25,38,30,50)(26,41,44,40)(27,45,43,31)(29,47,48,36)(35,53,49,42)(37,39,46,51);(22,24,28,34)(23,29,32,48)(25,39,30,51)(26,42,44,53)(27,46,43,37)(31,35,45,49)(33,40,52,41)(36,50,47,38);(19,21)(24,34)(29,48)(33,52)(35,49)(36,47)(37,46)(39,51)(42,53);(22,25,28,30)(23,26,32,44)(24,35,34,49)(27,41,43,40)(29,37,48,46)(31,50,45,38)(33,47,52,36)(39,53,51,42)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26832);