Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#12657 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C42 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#97 |
| prime radical | C23×C17 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
334 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)(24,34,37,49)(25,30)(26,31)(27,42)(28,33)(29,36,45,50)(32,43)(35,46,38,52)(39,53,51,44)(40,47)(41,48);(19,21)(22,24,27,38,26,36,40,51,28,37,43,35,41,50,25,39)(23,29,32,44,31,34,30,46,33,45,42,53,48,49,47,52);(22,25,26,27,28,40,41,43)(23,30,31,42,33,47,48,32)(24,35,50,51,37,38,36,39)(29,44,49,52,45,53,34,46)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5645);