Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#8417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #379 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
706 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)(19,22,23,24)(26,27,30,35,32,29,31,34)(28,36,39,37,40,41,38,33);(18,19)(20,24)(21,23)(22,25)(26,28)(27,33)(29,37)(30,39)(31,38)(32,40)(34,41)(35,36);(26,29,32,27)(28,37,40,33)(30,35,31,34)(36,38,41,39)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1405);