Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32944 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#33126 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C24×C67 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G | |
742 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)(3,5)(4,6)(7,8)(9,10,14,16)(11,19,21,33)(12,24,26,17)(13,27,20,18)(15,28,30,23)(22,36,35,32)(25,31,34,39)(29,37,38,40)(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);(1,3,4,7)(2,5,6,8)(9,11,20,28,14,21,13,23)(10,15,27,33,16,30,18,19)(12,22,34,40,26,35,25,37)(17,29,39,36,24,38,31,32);(2,6)(5,8)(10,16)(11,21)(17,24)(18,27)(22,35)(23,28)(31,39)(37,40);(9,12,13,25,14,26,20,34)(10,17,18,31,16,24,27,39)(11,22,23,37,21,35,28,40)(15,29,19,32,30,38,33,36)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26114);