Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#24810 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,46,25,30,24,29)(20,31,34,26,36,50,35,51)(21,37,47,27,41,54,40,55)(22,42,43,28,45,70,44,56)(32,48,38,52,60,74,59,73)(33,61,62,57,64,49,63,75)(39,53,71,69,68,77,67,65)(58,76,66,80,79,81,78,72);(18,20,23,34,25,36,24,35)(19,26,29,31,30,51,46,50)(21,38,40,32,41,59,47,60)(22,33,43,62,45,64,44,63)(27,52,54,74,55,73,37,48)(28,49,42,57,56,61,70,75)(39,66,67,58,68,78,71,79)(53,76,69,80,77,81,65,72);(18,21)(19,27)(20,32)(22,39)(23,40)(24,47)(25,41)(26,48)(28,53)(29,54)(30,55)(31,52)(33,58)(34,59)(35,38)(36,60)(37,46)(42,69)(43,67)(44,71)(45,68)(49,72)(50,73)(51,74)(56,77)(57,76)(61,80)(62,78)(63,66)(64,79)(65,70)(75,81);(18,22,24,44,25,45,23,43)(19,28,46,70,30,56,29,42)(20,33,35,63,36,64,34,62)(21,39,47,71,41,68,40,67)(26,49,50,75,51,61,31,57)(27,53,37,65,55,77,54,69)(32,58,38,66,60,79,59,78)(48,72,73,81,74,80,52,76)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17798);