Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#18462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
1030 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(19,24)(20,28)(21,33)(25,38)(26,36)(27,34)(29,32)(31,46)(35,45)(37,42)(39,49)(40,48)(41,47)(43,44);(18,19)(20,25)(21,34)(22,27)(23,26)(24,33)(28,42)(29,39)(30,40)(31,47)(32,41)(35,48)(36,45)(37,44)(38,46)(43,49);(20,29)(21,35)(24,36)(25,39)(28,32)(31,43)(33,45)(34,48)(37,38)(41,42)(44,46)(47,49);(18,20,30,28)(19,25,40,42)(21,31,45,43)(22,29,23,32)(24,37,48,38)(26,41,27,39)(33,44,35,46)(34,47,36,49)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11450);