Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#33435 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C53 | C24 |
| 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×C8×C53 ◁ G | |
674 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)(5,6,9,14,10,15,12,26,11,16,24,31,25,7,17,19)(8,20,22,34,23,18,27,33,21,13,28,29,35,30,32,36)(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)(8,21)(13,20)(18,30)(22,28)(23,35)(27,32)(29,34)(33,36);(5,7,9,19,10,6,12,14,11,15,24,26,25,16,17,31)(8,18,22,33,23,13,27,29,21,30,28,36,35,20,32,34);(5,8)(6,13)(7,18)(9,22)(10,23)(11,21)(12,27)(14,29)(15,30)(16,20)(17,32)(19,33)(24,28)(25,35)(26,36)(31,34)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26423);