Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#33701 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| socle | C22×C67 | C22×D8 |
| prime radical | C67×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C42×C67 ◁ C2×C4×C8×C67 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,24)(12,17)(13,19)(14,33)(15,35)(16,23)(18,27)(20,31)(21,34)(22,32)(25,37)(26,38)(28,36)(29,40)(30,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,5)(6,8)(9,11,15,26,13,25,14,12,16,27,31,28,32,29,34,30)(10,17,21,37,22,38,20,24,23,39,33,40,19,36,35,18);(1,3,4,7)(2,6,5,8)(9,12,14,29,32,26,15,27,16,30,34,25,13,28,31,11)(10,18,20,38,19,40,21,17,23,24,35,36,22,37,33,39);(9,13,16,32)(10,19,23,22)(11,25,27,29)(12,28,30,26)(14,31,34,15)(17,36,39,38)(18,40,24,37)(20,21,35,33)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26689);