Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#34291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2912 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(23,25)(26,27,31,35)(28,34,30,32)(29,33,38,41)(36,40,37,39);(26,28,31,30)(27,32,35,34)(29,37,38,36)(33,40,41,39);(22,23)(24,25)(26,27)(28,32)(29,33)(30,34)(31,35)(36,39)(37,40)(38,41);(26,29,31,38)(27,33,35,41)(28,36,30,37)(32,39,34,40);(18,20,21,19)(26,30,31,28)(27,34,35,32)(29,37,38,36)(33,40,41,39)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27279);