Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#18434 |
| 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 | |
982 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)(21,32)(25,37)(26,35)(27,33)(29,41)(31,45)(34,44)(36,40)(38,48)(39,47)(42,43)(46,49);(18,19)(20,25)(21,33)(22,27)(23,26)(24,32)(28,40)(29,38)(30,39)(31,46)(34,47)(35,44)(36,43)(37,45)(41,49)(42,48);(20,29)(21,34)(24,35)(25,38)(28,41)(31,45)(32,44)(33,47)(36,48)(37,46)(40,49)(42,43);(18,20,30,41)(19,25,39,49)(21,31,44,45)(22,29,23,28)(24,36,47,48)(26,40,27,38)(32,43,34,42)(33,46,35,37)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11422);