Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12979 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #120 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1869 |
| prime radical | C17×#575 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ 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)(18,19,23,29,24,30,44,57,25,31,45,58,22,28,42,55)(20,26,34,48,33,47,64,75,35,49,66,77,40,53,70,79)(21,36,39,68,38,51,69,56,37,54,43,71,41,27,50,52)(32,59,62,80,63,46,72,74,60,67,65,81,61,73,78,76);(18,20,23,34,24,33,44,64,25,35,45,66,22,40,42,70)(19,26,29,48,30,47,57,75,31,49,58,77,28,53,55,79)(21,32,43,65,38,63,50,78,37,60,39,62,41,61,69,72)(27,46,56,76,36,67,71,80,51,73,52,74,54,59,68,81);(18,21)(19,27)(20,32)(22,41)(23,43)(24,38)(25,37)(26,46)(28,54)(29,56)(30,36)(31,51)(33,63)(34,65)(35,60)(39,45)(40,61)(42,69)(44,50)(47,67)(48,76)(49,73)(52,58)(53,59)(55,68)(57,71)(62,66)(64,78)(70,72)(74,77)(75,80)(79,81)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5967);