Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
948 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)(18,19,23,21)(20,28,32,44)(22,35,37,47)(24,26,39,33)(25,40,29,30)(27,42,34,38)(31,43,46,48)(36,41,49,45);(18,20,24,31)(19,25,26,41)(21,29,33,45)(22,36,38,30)(23,32,39,46)(27,43,35,28)(34,48,47,44)(37,49,42,40);(18,21)(19,23)(20,29)(22,27)(24,33)(25,32)(26,39)(28,30)(31,45)(34,37)(35,38)(36,43)(40,44)(41,46)(42,47)(48,49);(19,26)(21,33)(25,41)(27,35)(28,43)(29,45)(34,47)(44,48)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11251);