Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19697 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#19708 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
738 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,6,9)(3,10,8,5)(4,7,12,14)(11,16,15,13)(17,18)(19,26)(20,24)(21,30)(22,25)(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);(1,3,5,2,6,8,10,9)(4,11,13,7,12,15,16,14)(19,27)(23,31)(26,32)(28,29);(1,4)(2,7)(3,11)(5,13)(6,12)(8,15)(9,14)(10,16)(17,19,21,29,22,27,20,28)(18,23,24,26,25,31,30,32);(4,12)(7,14)(11,15)(13,16)(17,20,22,21)(18,24,25,30)(19,28,27,29)(23,26,31,32)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 12696);