Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#33434 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C53 | C23 |
| commutator | C22 | C23×C8×C53 |
| Frattini, cosocle | C2×C8 | C24×C53 |
| socle | C22×C53 | C23×C8 |
| prime radical | C53×#532 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C53 ◁ G | |
690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(3,4)(5,6,8,12,9,13,19,25,10,14,20,26,21,27,32,35)(7,15,17,28,18,29,31,36,16,11,22,23,30,24,33,34)(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);(2,4)(7,16)(11,15)(17,22)(18,30)(23,28)(24,29)(31,33)(34,36);(5,6,8,12,9,13,19,25,10,14,20,26,21,27,32,35)(7,11,17,23,18,24,31,34,16,15,22,28,30,29,33,36);(5,7)(6,11)(8,17)(9,18)(10,16)(12,23)(13,24)(14,15)(19,31)(20,22)(21,30)(25,34)(26,28)(27,29)(32,33)(35,36)5936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26422);