Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C22×C4 |
| direct product | C67×#26034 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C67 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C4×C4⋊C4×C67 ◁ G | |
660 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 17152 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(3,7)(4,5)(6,8)(9,10,12,14)(11,15,16,13)(17,18)(19,26)(20,30)(21,25)(22,24)(23,29)(27,32)(28,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(2,5)(6,7)(17,19,21,29)(18,23,25,26)(20,28,22,27)(24,31,30,32);(9,11,12,16)(10,13,14,15)(19,27)(20,22)(23,31)(24,30)(26,32)(28,29);(1,3,4,8)(2,6,5,7)(17,20,21,22)(18,24,25,30)(19,28,29,27)(23,31,26,32)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 19022);