Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#34268 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2946 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)(26,27)(28,29)(30,38)(31,32)(33,36)(34,39)(35,40)(37,41);(22,23,25,24)(27,32)(29,33)(34,38)(37,40);(18,19)(20,21)(22,24,25,23)(26,28)(27,33)(29,32)(30,35)(31,36)(34,40)(37,38)(39,41);(26,29,31,33)(27,28,32,36)(30,37,39,40)(34,35,38,41);(26,30,31,39)(27,34,32,38)(28,35,36,41)(29,37,33,40)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27256);