Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#578 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
1302 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)(18,19,20,21)(22,23,28,32)(24,34,37,44)(25,38,42,30)(26,36,29,45)(27,33,46,31)(35,51,53,48)(39,47,52,40)(41,49,43,50);(22,24,28,37)(23,29,32,26)(25,39,42,52)(27,45,46,36)(30,48,38,51)(31,44,33,34)(35,41,53,43)(40,49,47,50);(19,21)(22,25,28,42)(23,30,32,38)(24,35,37,53)(26,40,29,47)(27,41,46,43)(31,49,33,50)(34,48,44,51)(36,52,45,39);(22,26)(23,24)(25,40)(27,34)(28,29)(30,35)(31,45)(32,37)(33,36)(38,53)(39,49)(41,48)(42,47)(43,51)(44,46)(50,52)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17450);