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×#18347 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3490 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1072 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)(18,19,22,27)(20,28,29,42)(21,32,35,26)(23,25,36,41)(24,33,39,30)(31,43,45,44)(34,47,49,40)(37,46,38,48);(18,20)(19,24)(21,33)(22,29)(23,31)(25,38)(26,42)(27,39)(28,32)(30,35)(34,48)(36,45)(37,41)(40,44)(43,47)(46,49);(21,34)(26,40)(28,43)(30,46)(32,47)(33,48)(35,49)(42,44);(19,25)(20,29)(24,37)(26,40)(27,41)(28,44)(30,33)(31,45)(32,47)(38,39)(42,43)(46,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11335);