Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#20203 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| prime radical | C67×#3274 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C42×C67 ◁ G | |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,5,8)(3,6,4,7)(9,10,14,18)(11,16,13,15)(12,17,20,24)(19,23,21,22)(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)(2,6,8,7)(10,15)(11,13)(12,19)(16,18)(17,24)(20,21);(2,7)(3,4)(6,8)(9,11,14,13)(10,16,18,15)(12,19,20,21)(17,23,24,22);(9,12,14,20)(10,17,18,24)(11,19,13,21)(15,22,16,23)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13191);