Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#10868 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #117 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #382 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C17×#117 ◁ G | |
730 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)(24,33,36,29)(25,38)(26,42)(27,32)(28,31)(30,39)(34,48,50,52)(35,44,37,47)(40,45)(41,53)(43,49,46,51);(19,21)(22,24,27,37,28,36,26,35)(23,29,32,44,31,33,42,47)(25,34,40,51,41,50,39,49)(30,43,38,52,45,46,53,48);(22,25,26,39,28,41,27,40)(23,30,32,38,31,45,42,53)(24,34,35,49,36,50,37,51)(29,43,44,52,33,46,47,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3856);