Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33608 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ C2×C17×#131 ◁ G | |
650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,28,33)(24,34,39,59)(25,30,40,51)(26,43,45,71)(27,46,44,32)(29,47,50,37)(31,54,55,35)(36,56,62,78)(38,66,65,58)(41,69,67,84)(42,70,68,53)(48,72,74,63)(49,60,57,73)(52,77,76,61)(64,83,82,80)(75,81,79,85);(22,24,35,60,27,38,45,47,28,39,54,73,44,65,26,37)(23,29,43,58,32,49,55,59,33,50,71,66,46,57,31,34)(25,36,61,81,42,64,67,72,40,62,77,85,68,82,41,63)(30,48,69,80,53,75,76,78,51,74,84,83,70,79,52,56);(19,21)(22,25)(23,30)(24,36)(26,41)(27,42)(28,40)(29,48)(31,52)(32,53)(33,51)(34,56)(35,61)(37,63)(38,64)(39,62)(43,69)(44,68)(45,67)(46,70)(47,72)(49,75)(50,74)(54,77)(55,76)(57,79)(58,80)(59,78)(60,81)(65,82)(66,83)(71,84)(73,85);(25,40)(30,51)(36,62)(41,67)(42,68)(48,74)(52,76)(53,70)(56,78)(61,77)(63,72)(64,82)(69,84)(75,79)(80,83)(81,85)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26596);