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×#18154 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#392 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
960 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)(21,31)(25,37)(26,35)(27,32)(30,42)(33,44)(36,39)(38,47)(40,45)(46,48);(18,19,22,27)(20,25,28,39)(21,32,31,24)(23,26,34,40)(29,37,41,36)(30,38,42,48)(33,45,44,35)(43,47,49,46);(21,33)(24,35)(29,43)(31,44)(32,45)(36,46)(37,47)(41,49);(18,20,23,30)(19,25,26,38)(21,29,33,43)(22,28,34,42)(24,36,35,46)(27,39,40,48)(31,41,44,49)(32,37,45,47)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11142);