Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#2635 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
996 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)(19,24)(20,28)(21,32)(25,38)(26,36)(27,33)(29,44)(30,46)(31,43)(34,48)(37,39)(40,49)(41,45)(42,47);(18,19,22,27)(20,29,31,25)(21,33,32,24)(23,26,35,40)(28,41,43,39)(30,37,47,45)(34,49,48,36)(38,46,44,42);(21,34)(24,36)(30,42)(32,48)(33,49)(37,38)(44,45)(46,47);(18,20,22,31)(19,25,27,29)(21,30,32,47)(23,28,35,43)(24,37,33,45)(26,39,40,41)(34,42,48,46)(36,38,49,44)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11340);