Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9263 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#9273 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#3205 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
560 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)(18,19,20,24,22,25,21,23)(27,31)(28,35)(29,32)(34,39)(36,37)(38,40);(19,23)(20,21)(24,25)(26,27,32,39,30,34,29,31)(28,33,35,40,37,41,36,38);(19,24)(20,21)(23,25)(26,28)(27,33)(29,36)(30,37)(31,38)(32,35)(34,41)(39,40)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2261);