Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11295 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #400 |
| prime radical | C24×C17 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
574 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)(22,23,27,32,28,33,26,31)(24,34,37,29,38,45,36,46)(25,39,41,30,43,48,42,49)(35,51,52,47,53,44,40,50);(18,19)(20,21)(22,24,26,37,28,38,27,36)(23,29,31,45,33,46,32,34)(25,40,42,35,43,52,41,53)(30,47,39,44,49,50,48,51);(19,21)(22,25,26,41,28,43,27,42)(23,30,31,48,33,49,32,39)(24,35,36,52,38,53,37,40)(29,44,34,50,46,51,45,47)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4283);