Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24295 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1302 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)(18,19)(20,22)(21,34)(23,42)(24,29)(25,30)(26,32)(27,38)(28,40)(31,43)(33,41)(35,36)(37,45)(39,44)(46,49)(47,48);(18,20,23,32,25,33,24,28)(19,26,29,22,30,40,42,41)(21,35,37,31,39,46,38,47)(27,36,44,48,45,49,34,43);(18,21)(19,27)(20,31)(22,36)(23,37)(24,38)(25,39)(26,43)(28,35)(29,44)(30,45)(32,46)(33,47)(34,42)(40,48)(41,49);(18,22,23,40,25,41,24,26)(19,28,29,20,30,32,42,33)(21,36,37,48,39,49,38,43)(27,35,44,31,45,46,34,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17283);