Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#25051 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C67×#3060 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ G | |
736 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)(3,5)(4,6)(7,8)(9,10)(11,18)(12,22)(13,16)(14,17)(15,19)(20,23)(21,24)(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);(1,3,4,7)(2,5,6,8)(9,10,13,22,14,17,12,16)(11,15,20,24,21,23,19,18);(2,6)(5,8)(9,10)(11,15)(12,16)(13,22)(14,17)(18,19)(20,24)(21,23);(9,11,12,19,14,21,13,20)(10,15,16,18,17,23,22,24)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 18039);