Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#33883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| prime radical | C67×#3285 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C4×D4×C67 ◁ C8×D4×C67 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2,4,6)(3,7,8,5)(9,10,14,18)(11,19,20,37)(12,23,27,38)(13,28,25,17)(15,30,31,21)(16,33,35,26)(22,39,29,34)(24,36,40,32)(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);(1,3)(2,5)(4,8)(6,7)(11,20)(15,31)(19,37)(21,30)(22,29)(24,40)(32,36)(34,39);(9,11,14,20)(10,15,18,31)(12,24,27,40)(13,29,25,22)(16,34,35,39)(17,36,28,32)(19,38,37,23)(21,33,30,26);(3,8)(5,7)2881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26871);