Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#22307 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator | C22 | C23×C8×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle, prime radical | C23×C67 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 17152 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,6)(4,8)(5,7)(9,10)(11,13)(12,15)(14,16)(17,18,20,23,21,19,22,24)(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);(1,3,5,4)(2,6,7,8)(9,11,13,10)(12,15,16,14)(17,19,20,24,21,18,22,23);(1,4,5,3)(2,6,7,8)(10,11)(14,15);(9,12,13,16)(10,14,11,15)5896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 15295);