Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#17412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#120 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
1046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,26,23,27,32,39)(20,25,29,38,28,37,40,47)(22,24,31,35,33,36,43,46)(30,34,42,45,41,44,48,49);(19,24)(21,31)(25,34)(27,36)(29,42)(32,43)(37,44)(40,48);(18,20,22,30)(19,25,24,34)(21,29,31,42)(23,28,33,41)(26,38,35,45)(27,37,36,44)(32,40,43,48)(39,47,46,49);(20,28)(25,37)(29,40)(30,41)(34,44)(38,47)(42,48)(45,49)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10400);