Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#8817 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #127 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 4352 |
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)(24,30)(25,34)(26,28)(27,32)(29,31)(33,36)(35,37)(38,39)(40,46)(41,43)(42,50)(44,48)(45,49)(47,52)(51,53);(22,24,31,37,26,33,25,32)(23,27,34,36,28,35,29,30)(39,43)(44,51)(45,50)(46,52);(23,28)(27,35)(29,34)(30,36)(38,40,42,48,41,47,49,53)(39,44,45,46,43,51,50,52)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1805);