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×#33878 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| prime radical | C67×#3280 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C4×D4×C67 ◁ C8×D4×C67 ◁ G | |
562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,22)(13,26)(14,30)(15,19)(17,24)(18,28)(20,36)(21,35)(23,34)(25,38)(27,31)(29,40)(32,39)(33,37)(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)(9,11,15,14)(10,16,19,30)(12,23,25,20)(13,21,29,28)(17,32,33,31)(18,26,35,40)(22,34,38,36)(24,39,37,27);(9,12)(10,17)(11,20)(13,27)(14,23)(15,25)(16,31)(18,34)(19,33)(21,37)(22,26)(24,28)(29,39)(30,32)(35,36)(38,40);(3,8)(5,7)(9,11,15,14)(10,16,19,30)(12,20,25,23)(13,21,29,28)(17,31,33,32)(18,26,35,40)(22,36,38,34)(24,27,37,39)2881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26866);