Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8101 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C42 |
| direct product | C17×#8102 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#95 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C25 | C23×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C24×C4×C17 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(20,24)(21,23)(22,25)(26,27)(28,34,36,31)(29,37)(30,33)(32,38)(35,39,41,40);(18,20)(19,22,23,24)(21,25)(26,28)(27,31)(29,35)(30,36)(32,39)(33,34)(37,40)(38,41);(26,29,30,38)(27,32,33,37)(28,35,36,41)(31,39,34,40)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1090);