Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#18996 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| prime radical | C67×#3529 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
948 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 107 points:
(2,5)(3,7)(6,8)(9,10,15,20)(11,21,25,31)(12,26,28,34)(13,19,14,18)(16,23,32,24)(17,29,33,27)(22,30,38,40)(35,37,39,36)(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);(3,7)(5,8)(9,11)(10,16)(12,22)(13,23)(14,24)(15,25)(17,30)(18,31)(19,21)(20,32)(26,39)(27,36)(28,38)(29,37)(33,40)(34,35);(1,2)(3,8)(4,6)(5,7)(9,12)(10,17)(11,22)(13,27)(14,29)(15,28)(16,30)(18,26)(19,34)(20,33)(21,35)(23,36)(24,37)(25,38)(31,39)(32,40);(9,13,15,14)(10,18,20,19)(11,23,25,24)(12,27,28,29)(16,31,32,21)(17,26,33,34)(22,36,38,37)(30,39,40,35)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 11984);