Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C17 · Schur multiplier (H2) = C23×C43 |
| direct product | C17×#13761 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C17 | C23 |
| commutator | C22 | C22×C42×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| socle | C24×C17 | C24 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C17 ◁ G | |
2294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,24,25)(30,31)(32,35)(33,34)(36,37);(26,27,28,29)(31,34)(35,37);(18,19,20,21)(23,25);(30,32,33,36)(31,35,34,37)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6749);