Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C210 |
| direct product | C17×#34257 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×C17×2−1+4 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
5050 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)(19,21)(22,23,25,24)(27,28)(30,38)(32,34)(36,41);(26,27,31,28)(29,34,37,32)(30,33,38,35)(36,40,41,39);(18,19,20,21)(22,24,25,23)(26,28,31,27)(29,34,37,32)(30,35,38,33)(36,40,41,39);(26,29,31,37)(27,32,28,34)(30,36,38,41)(33,39,35,40);(26,30)(27,33)(28,35)(29,36)(31,38)(32,39)(34,40)(37,41)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27245);