Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19856 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#555 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(18,19,23,21)(20,26,30,33)(22,31,32,25)(24,28,27,29)(34,35)(36,40)(37,44)(38,46)(39,42)(41,43)(45,48)(47,49);(18,20,23,30)(19,24,21,27)(22,28,32,29)(25,33,31,26)(34,36,39,38)(35,40,42,46)(37,43,45,47)(41,48,49,44);(18,21,23,19)(20,27,30,24)(22,31,32,25)(26,29,33,28)(34,37)(35,41)(36,43)(38,47)(39,45)(40,48)(42,49)(44,46);(20,28)(22,32)(24,33)(25,31)(26,27)(29,30)(34,36,39,38)(35,40,42,46)(37,43,45,47)(41,48,49,44)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12844);