Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11305 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #397 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 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)(24,33)(25,30)(26,41)(27,32)(28,31)(29,35)(34,49)(36,50)(37,44)(38,43)(39,47)(40,48)(42,46)(45,51)(52,53);(22,24,28,37,27,36,26,35)(23,29,41,50,32,44,31,33)(25,38,39,51,40,52,42,34)(30,45,46,43,48,49,47,53);(22,25,26,39,27,40,28,42)(23,30,31,46,32,48,41,47)(24,34,35,38,36,51,37,52)(29,43,33,49,44,53,50,45)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4293);