Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×#466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
636 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)(18,19,25,31)(20,32,35,58)(21,39,42,56)(22,43,45,54)(23,30,24,29)(26,47,49,36)(27,46,53,41)(28,44,55,33)(34,63,64,80)(37,60,38,59)(40,71,72,52)(48,75,76,81)(50,67,51,61)(57,68,79,66)(62,70,73,78)(65,69,74,77);(18,20,33,61,24,38,45,47,25,35,44,67,23,37,22,36)(19,26,43,60,30,51,55,58,31,49,54,59,29,50,28,32)(21,34,62,81,41,66,72,74,42,64,73,75,46,68,40,65)(27,48,70,63,39,69,71,79,53,76,78,80,56,77,52,57);(18,21)(19,27)(20,34)(22,40)(23,46)(24,41)(25,42)(26,48)(28,52)(29,56)(30,39)(31,53)(32,57)(33,62)(35,64)(36,65)(37,68)(38,66)(43,70)(44,73)(45,72)(47,74)(49,76)(50,77)(51,69)(54,78)(55,71)(58,79)(59,80)(60,63)(61,81)(67,75);(20,35)(26,49)(32,58)(34,64)(36,47)(37,38)(48,76)(50,51)(57,79)(59,60)(61,67)(63,80)(65,74)(66,68)(69,77)(75,81)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26607);