Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C22×C4 |
| direct product | C67×#22312 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator | C23 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle, prime radical | C23×C67 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
610 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)(3,6)(4,8)(5,7)(9,10)(11,13)(12,15)(14,16)(17,18,23,19,22,26,21,25)(20,24,28,27,29,31,30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3,5,4)(2,6,7,8)(9,11,13,10)(12,15,16,14)(17,19,23,26,22,25,21,18)(20,27,28,31,29,32,30,24);(1,4,5,3)(2,6,7,8)(10,11)(14,15)(17,20,22,29)(18,24,26,31)(19,27,25,32)(21,30,23,28);(9,12,13,16)(10,14,11,15)(17,21,22,23)(18,25,26,19)(20,28,29,30)(24,27,31,32)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 15300);