Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#34201 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C2×C17×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
3118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
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)(19,21)(22,23,25,24)(26,27)(28,33)(29,34)(30,38)(31,32)(35,39)(36,37)(40,41);(22,24,25,23)(27,32)(29,33)(35,38)(37,40);(18,19)(20,21)(26,28,31,34)(27,33,32,29)(30,36,39,41)(35,40,38,37);(26,29,31,33)(27,34,32,28)(30,37,39,40)(35,41,38,36);(26,30)(27,35)(28,36)(29,37)(31,39)(32,38)(33,40)(34,41)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27189);