Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13033 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13035 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1879 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
456 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)(18,19,23,30,48,51,47,28,25,32,46,62,24,31,22,29)(20,33,37,26,49,53,35,63,39,66,73,55,38,60,36,54)(21,40,42,59,50,61,41,58,44,56,45,27,43,57,75,64)(34,52,69,77,74,80,68,76,71,79,72,65,70,78,67,81);(18,20,24,49,25,39,48,38)(19,26,51,54,32,55,31,63)(21,34,50,70,44,71,43,74)(22,37,46,35,47,73,23,36)(27,52,58,80,59,79,64,78)(28,60,62,66,29,53,30,33)(40,65,57,81,56,77,61,76)(41,72,45,68,75,69,42,67);(18,21)(19,27)(20,34)(22,45)(23,41)(24,50)(25,44)(26,52)(28,57)(29,61)(30,40)(31,64)(32,59)(33,65)(35,69)(36,72)(37,68)(38,74)(39,71)(42,47)(43,48)(46,75)(49,70)(51,58)(53,76)(54,80)(55,79)(56,62)(60,81)(63,78)(66,77)(67,73)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6023);