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×#10896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #121 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,25,24)(27,31)(28,34)(29,37)(33,39)(35,36)(38,40);(19,21)(26,27,29,31,30,33,37,39)(28,32,35,38,36,41,34,40);(22,24,25,23)(26,28)(27,32)(29,35)(30,36)(31,38)(33,41)(34,37)(39,40)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3884);