Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13417 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13418 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2041 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,34)(21,41)(22,32)(23,48)(24,30)(25,29)(26,33)(27,36)(28,44)(31,50)(35,67)(37,54)(38,55)(39,57)(40,56)(42,53)(43,60)(45,65)(46,78)(47,62)(49,59)(51,61)(52,77)(58,70)(63,71)(64,73)(66,69)(68,79)(72,80)(74,76)(75,81);(18,20,26,40)(19,27,33,57)(21,42,46,72)(22,39,25,36)(23,38,50,71)(24,37,47,73)(28,58,61,67)(29,56,32,34)(30,63,62,55)(31,64,48,54)(35,49,70,45)(41,76,78,66)(43,69,52,74)(44,68,51,75)(53,77,80,60)(59,81,65,79);(18,21,22,43,26,46,25,52)(19,28,29,59,33,61,32,65)(20,35,36,68,40,70,39,75)(23,49,47,44,50,45,24,51)(27,53,34,66,57,80,56,76)(30,60,31,41,62,77,48,78)(37,72,71,69,73,42,38,74)(54,58,55,79,64,67,63,81)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6406);