Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#33703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| prime radical | C2×#135×C67 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #117×C67 ◁ #405×C67 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10,16,21)(11,22,24,23)(12,28,18,14)(13,29,31,19)(15,32,30,20)(17,33,34,25)(26,36,39,37)(27,35,40,38)(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)(9,11,14,26,15,27,13,25,16,24,28,39,30,40,31,33)(10,17,19,35,20,36,18,22,21,34,29,38,32,37,12,23);(1,3,4,7)(2,6,5,8)(9,12,13,20,30,29,14,10,16,18,31,32,15,19,28,21)(11,23,25,36,40,38,26,17,24,22,33,37,27,35,39,34);(11,24)(17,34)(22,23)(25,33)(26,39)(27,40)(35,38)(36,37)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26691);