Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18208 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#1595 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
994 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)(25,38)(26,36)(27,33)(29,37)(31,42)(34,45)(39,48)(40,46)(43,47);(18,19)(20,29)(21,33)(22,27)(23,26)(24,32)(25,28)(30,37)(31,43)(34,46)(35,40)(36,45)(38,41)(39,42)(44,47)(48,49);(21,34)(24,36)(30,44)(32,45)(33,46)(37,47)(38,48)(41,49);(18,20,23,31)(19,25,26,39)(21,30,34,44)(22,28,35,42)(24,37,36,47)(27,29,40,43)(32,41,45,49)(33,38,46,48)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11196);