Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18436 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3558 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
972 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(20,24)(21,23)(22,26)(25,29)(27,31)(28,30)(32,33)(34,35,39,43)(36,44,46,49)(37,42,38,41)(40,47,48,45);(19,23)(21,29)(24,30)(25,26)(28,33)(31,32)(34,36)(35,40)(37,45)(38,47)(39,46)(41,44)(42,49)(43,48);(18,20)(19,24)(21,28)(22,27)(23,30)(25,32)(26,31)(29,33)(37,38)(41,42)(44,49)(45,47);(20,27)(24,31)(28,33)(30,32)(34,37,39,38)(35,41,43,42)(36,45,46,47)(40,44,48,49)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11424);