Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C22 |
| direct product | C67×#9551 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #121 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| socle | C22×C67 | #388 |
| prime radical | C23×C67 | #117 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C42×C67 ◁ G | |
334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,5,7,4,3,6,8)(10,14)(11,17)(12,19)(15,22)(16,21)(20,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,5,8,4,2,6,7)(9,10,12,14,13,16,19,21)(11,15,18,20,17,23,24,22);(2,3)(7,8)(9,11,12,18,13,17,19,24)(10,15,14,20,16,23,21,22)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 2539);