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×#13034 |
| 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 | |
462 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)(18,19,23,28,24,30,49,61,25,31,22,29,45,60,46,64)(20,32,35,53,36,58,47,54,37,68,34,65,50,62,43,26)(21,38,40,66,41,59,44,27,42,55,39,56,51,63,48,57)(33,52,70,76,71,77,73,80,72,78,69,81,75,79,74,67);(18,20)(19,26,31,54)(21,33)(22,43)(23,47)(24,50)(25,37)(27,52,57,78)(28,58,29,62)(30,65,60,53)(32,64,68,61)(34,46)(35,49)(36,45)(38,67,55,80)(39,74)(40,73)(41,75)(42,72)(44,70)(48,69)(51,71)(56,79,66,77)(59,81,63,76);(18,21,25,42)(19,27,31,57)(20,33,37,72)(22,44,23,48)(24,51,45,41)(26,52,54,78)(28,59,29,63)(30,66,60,56)(32,67,68,80)(34,73,35,74)(36,75,50,71)(38,64,55,61)(39,46,40,49)(43,70,47,69)(53,79,65,77)(58,81,62,76)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6022);