Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3060 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,29)(21,35)(22,27)(23,41)(24,28)(25,32)(26,39)(30,37)(31,46)(33,47)(34,43)(36,38)(40,49)(42,48)(44,45);(18,19)(20,30)(21,36)(22,41)(23,27)(24,28)(25,33)(26,40)(29,45)(31,44)(32,43)(34,42)(35,38)(37,46)(39,49)(47,48);(18,20,23,33,24,31,22,34)(19,25,27,44,28,42,41,30)(21,37,39,48,40,45,38,32)(26,43,35,46,36,47,49,29)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6388);