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×#19798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#459 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
592 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)(20,26,28,33)(22,30,32,25)(24,31,29,27)(34,35,38,42)(36,39,44,48)(37,40,45,41)(43,46,49,47);(18,20,23,28)(19,24,21,29)(22,31,32,27)(25,33,30,26)(34,36,38,44)(35,39,42,48)(37,43,45,49)(40,46,41,47);(35,40)(37,45)(39,46)(41,42)(43,49)(47,48);(18,21,23,19)(20,26,28,33)(22,25,32,30)(24,31,29,27)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12786);