Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18149 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1074 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)(18,19,24,28)(20,29,31,44)(21,26,34,43)(22,35,37,46)(23,27,33,42)(25,38,41,30)(32,39,45,49)(36,40,47,48);(18,20)(19,25)(21,30)(22,36)(23,32)(24,31)(26,39)(27,40)(28,41)(29,35)(33,45)(34,38)(37,47)(42,48)(43,49)(44,46);(18,21,33,37)(19,26,42,46)(20,30,45,47)(22,24,34,23)(25,39,48,44)(27,35,28,43)(29,41,49,40)(31,38,32,36);(19,27)(25,40)(26,35)(28,42)(29,39)(41,48)(43,46)(44,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11137);