Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8603 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#11260 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #117 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C22×C67 | #382 |
| prime radical | C24×C67 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×#117×C67 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 103 points:
(5,6,10,16,11,14,9,15)(7,17,19,29,20,12,24,27)(8,21,22,28,23,30,25,13)(18,32,34,31,35,36,33,26)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,2)(3,4)(5,7,9,19,11,20,10,24)(6,12,15,27,14,17,16,29)(8,18,22,33,23,35,25,34)(13,26,21,36,28,31,30,32);(2,4)(5,8)(6,13,14,28)(7,18)(9,22)(10,25)(11,23)(12,26,17,31)(15,21,16,30)(19,33)(20,35)(24,34)(27,36,29,32)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 4248);