Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34395 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C2×C17×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
1990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 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)(23,27)(24,30)(29,34)(31,36)(38,39,42,43)(40,46,47,44)(41,49,50,45)(48,51,53,52);(23,27)(28,33)(29,34)(35,37)(39,43)(40,47)(45,49)(48,53);(22,23,26,27)(24,28,30,33)(25,29,32,34)(31,35,36,37)(38,39)(40,44)(41,45)(42,43)(46,47)(48,51)(49,50)(52,53);(22,24)(23,28)(25,31)(26,30)(27,33)(29,35)(32,36)(34,37)(38,40,42,47)(39,44,43,46)(41,48,50,53)(45,51,49,52);(22,25,26,32)(23,29,27,34)(24,31,30,36)(28,35,33,37)(38,41,42,50)(39,45,43,49)(40,48,47,53)(44,51,46,52)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27383);