Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#20096 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| prime radical | #550×C67 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C42×C67 ◁ G | |
592 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,5,9)(3,7,11,15)(4,6,12,8)(10,16,13,14)(17,18,21,24)(19,25,26,32)(20,28,30,23)(22,29,31,27)(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);(2,6)(3,10)(4,12)(7,15)(8,9)(11,13)(19,26)(22,31)(25,32)(27,29);(17,19,21,26)(18,22,24,31)(20,29,30,27)(23,32,28,25);(1,3,5,11)(2,7,9,15)(4,13,12,10)(6,14,8,16)2479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13084);