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×#18441 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3559 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
888 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)(18,19,22,26)(20,24,27,31)(21,23,29,25)(28,30,33,32)(35,40)(37,38)(41,48)(42,46)(43,44)(47,49);(19,23)(21,29)(24,30)(25,26)(28,33)(31,32)(34,35)(36,41)(37,40)(38,46)(39,42)(43,48)(44,47)(45,49);(18,20,22,27)(19,24,26,31)(21,28,29,33)(23,30,25,32)(34,36,39,45)(35,41,42,49)(37,44,38,43)(40,47,46,48);(20,27)(24,31)(28,33)(30,32)(34,37,39,38)(35,40,42,46)(36,43,45,44)(41,48,49,47)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11429);