Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C23 |
| direct product | C67×#8998 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #120 |
| commutator | C42 | C22×C4×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| socle | C22×C67 | #386 |
| prime radical | #121×C67 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C42×C67 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2)(3,10,14,16)(4,13,15,7)(5,8)(6,9)(11,12)(17,18)(19,25,27,32)(20,22)(21,24)(23,26,30,29)(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);(1,3,11,13,6,14,5,7)(2,4,12,10,9,15,8,16)(18,22)(21,28)(23,30)(26,29);(1,4)(2,7)(3,12)(5,16)(6,15)(8,14)(9,13)(10,11)(17,19)(18,23)(20,27)(21,29)(22,30)(24,32)(25,31)(26,28)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 1986);