Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#19150 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| socle | C22×C67 | C2×#121 |
| prime radical | C23×C67 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C42×C67 ◁ G | |
586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(3,10)(4,8)(5,14)(6,9)(7,13)(11,16)(12,15)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26)(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);(1,3,5,13,6,11,4,12)(2,7,8,10,9,15,14,16);(3,11)(7,15)(10,16)(12,13)(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25);(1,4,6,5)(2,8,9,14)(3,12,11,13)(7,10,15,16)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 12138);