Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#20221 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C67 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C42×C67 ◁ G | |
542 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 17152 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,7,5)(3,10,13,16)(4,9,6,14)(8,11,15,12)(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);(1,3,7,13)(2,8,5,15)(4,12,6,11)(9,16,14,10)(19,26)(22,31)(25,32)(27,29);(1,4,7,6)(2,9,5,14)(3,11,13,12)(8,10,15,16)(17,19,21,26)(18,22,24,31)(20,29,30,27)(23,32,28,25);(1,5,7,2)(3,10,13,16)(4,14,6,9)(8,11,15,12)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13209);