Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C27 |
| direct product | C67×#36700 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C67 |
| socle | C23×C67 | C25 |
| prime radical | C24×C67 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
1356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(3,6)(4,8)(5,7)(9,10)(11,15)(12,16)(13,14)(17,20)(18,22)(19,21)(23,24)(25,26,29,32)(27,30,34,38)(28,31,36,40)(33,37,35,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3,5,4)(2,6,7,8)(10,14)(15,20)(16,21)(22,24)(25,27,29,34)(26,30,32,38)(28,35,36,33)(31,39,40,37);(2,7)(6,8)(9,11)(10,15)(12,18)(13,17)(14,20)(16,22)(19,23)(21,24)(25,28)(26,31)(27,33)(29,36)(30,37)(32,40)(34,35)(38,39);(1,4,5,3)(2,8,7,6)(11,17)(15,20)(18,23)(22,24)(26,32)(28,36)(30,38)(33,35);(9,12,13,19)(10,16,14,21)(11,18,17,23)(15,22,20,24)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 29688);