Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#1600 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
932 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)(21,32)(25,36)(26,35)(27,33)(30,40)(34,42)(37,43)(38,46)(39,47)(44,45)(48,49);(18,19,22,27)(20,25,28,37)(21,33,32,24)(23,26,29,38)(30,43,40,36)(31,39,41,49)(34,46,42,35)(44,47,45,48);(20,28)(21,34)(24,35)(25,37)(30,44)(31,41)(32,42)(33,46)(36,48)(39,49)(40,45)(43,47);(18,20,29,41)(19,25,38,49)(21,30,42,44)(22,28,23,31)(24,36,46,48)(26,39,27,37)(32,40,34,45)(33,43,35,47)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11238);