Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32941 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#33221 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×#41×C67 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
706 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)(9,10,13,16)(11,21,23,33)(12,26,27,34)(14,20,15,19)(17,25,30,24)(18,29,31,28)(22,36,37,32)(35,39,40,38)(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);(1,3,4,8)(2,5,6,7)(10,16)(17,30)(18,31)(19,20)(21,33)(26,34)(32,36)(35,40);(9,11,14,24,13,23,15,25)(10,17,19,21,16,30,20,33)(12,22,28,38,27,37,29,39)(18,32,26,35,31,36,34,40);(9,12)(10,18)(11,22)(13,27)(14,28)(15,29)(16,31)(17,32)(19,26)(20,34)(21,35)(23,37)(24,38)(25,39)(30,36)(33,40)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26209);