Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C42 |
| direct product | C17×#14659 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| prime radical | C22×C17×#121 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
2222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(27,30)(31,33)(34,35)(36,39)(37,38)(40,41);(19,21)(22,23,24,25)(27,30)(28,32)(35,38)(36,40);(18,19)(20,21)(22,23)(24,25)(26,27)(28,31)(29,30)(32,33)(34,35)(36,41)(37,38)(39,40);(26,28)(27,31)(29,32)(30,33)(34,36,37,40)(35,39,38,41)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 7647);