Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18377 |
| 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 | |
1082 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)(20,29,30,42)(21,33,36,26)(23,28,37,25)(24,34,39,31)(32,44,45,49)(35,41,48,43)(38,47,40,46);(18,20)(19,24)(21,34)(22,30)(23,32)(25,40)(26,42)(27,39)(28,38)(29,33)(31,36)(35,47)(37,45)(41,44)(43,49)(46,48);(21,35)(26,43)(29,44)(31,46)(33,41)(34,47)(36,48)(42,49);(19,25)(20,30)(24,38)(26,41)(27,28)(29,44)(31,34)(32,45)(33,43)(39,40)(42,49)(46,47)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11365);