Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#25442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C67×#3061 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ G | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 103 points:
(5,6,9,12,11,16,10,15)(7,17,18,13,21,28,20,29)(8,22,23,14,25,26,24,30)(19,27,32,35,34,36,33,31)(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)(6,12,16,15)(7,18,21,20)(14,26,30,22)(19,32,34,33);(2,4)(5,7)(6,13)(8,19)(9,20)(10,18)(11,21)(12,17)(14,27)(15,28)(16,29)(22,35)(23,33)(24,32)(25,34)(26,31)(30,36);(5,8,10,24,11,25,9,23)(6,14,12,26,16,30,15,22)(7,19,18,32,21,34,20,33)(13,27,17,31,29,36,28,35)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 18430);