Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32941 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#33062 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×AGL(1,ℤ/8)×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
764 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,21)(12,16)(13,27)(14,31)(15,20)(17,24)(18,29)(19,22)(23,32)(25,34)(26,33)(28,36)(30,35)(37,38)(39,40)(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);(2,5)(6,8)(9,11,22,26,15,24,14,12)(10,16,31,17,20,33,19,21)(13,23,29,38,30,39,28,25)(18,32,27,34,36,40,35,37);(1,3,4,7)(2,6,5,8)(9,12,14,24,15,26,22,11)(10,17,19,16,20,21,31,33)(13,25,28,39,30,38,29,23)(18,34,35,32,36,37,27,40);(9,13)(10,18)(11,23)(12,25)(14,28)(15,30)(16,32)(17,34)(19,35)(20,36)(21,37)(22,29)(24,39)(26,38)(27,31)(33,40)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26050);