Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60372 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#60583 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | #525×C67 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×#117×C67 ◁ G | |
1998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10,14,18)(11,19,22,32)(12,16,23,30)(13,25,27,17)(15,26,29,21)(20,33,34,40)(24,37,36,31)(28,38,39,35)(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);(9,11,14,22)(10,15,18,29)(12,20,23,34)(13,26,27,21)(16,28,30,39)(17,32,25,19)(24,38,36,35)(31,40,37,33);(1,3,4,7)(2,6,5,8)(9,12)(10,16)(11,20)(13,24)(14,23)(15,28)(17,31)(18,30)(19,33)(21,35)(22,34)(25,37)(26,38)(27,36)(29,39)(32,40);(12,23)(16,30)(20,34)(24,36)(28,39)(31,37)(33,40)(35,38)4087 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53571);