Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#11027 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #121 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C23×D8×C17 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
1498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
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)(20,21)(26,27,30,35,31,33,29,34)(28,36,37,40,39,32,38,41);(19,21)(22,23)(24,25)(26,28)(27,32)(29,37)(30,38)(31,39)(33,36)(34,41)(35,40);(23,25)(27,33)(28,37)(29,30)(32,40)(36,41)(38,39)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4015);