Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19906 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3358 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
608 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)(19,23)(21,29)(24,30)(25,32)(26,33)(27,31)(34,35)(36,39)(37,40)(38,42)(41,45)(43,46)(44,48)(47,49);(18,19,22,24)(20,26,28,32)(21,30,29,23)(25,31,33,27)(34,36,38,44)(35,39,42,48)(37,43,45,49)(40,46,41,47);(19,24)(23,30)(25,33)(26,32)(35,40)(37,45)(39,46)(41,42)(43,49)(47,48);(18,20,22,28)(19,25,24,33)(21,31,29,27)(23,32,30,26)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12894);