Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13339 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,29,35)(24,36,41,71)(25,42,48,61)(26,49,54,67)(27,34,28,33)(30,55,59,38)(31,44,64,45)(32,52,68,53)(37,56,75,84)(39,65,40,70)(43,80,74,60)(46,66,47,79)(50,57,77,58)(51,62,82,63)(69,72,85,73)(76,78,81,83);(18,19)(20,21)(22,24,29,41)(23,30,35,59)(25,43,48,74)(26,50,54,77)(27,40,28,39)(31,60,64,80)(32,65,68,70)(33,58,34,57)(36,67,71,49)(37,47,75,46)(38,52,55,53)(42,78,61,83)(44,72,45,73)(51,81,82,76)(56,63,84,62)(66,85,79,69);(19,21)(22,25)(23,31)(24,37)(26,51)(27,47)(28,46)(29,48)(30,56)(32,66)(33,63)(34,62)(35,64)(36,69)(38,76)(39,74)(40,43)(41,75)(42,49)(44,52)(45,53)(50,73)(54,82)(55,81)(57,80)(58,60)(59,84)(61,67)(65,78)(68,79)(70,83)(71,85)(72,77)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6327);