Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#21678 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C53 | C24 |
| commutator | C23 | C23×C4×C53 |
| Frattini, cosocle | C22×C4 | C24×C53 |
| socle, prime radical | C23×C53 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C53 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(3,5)(4,6)(7,8)(9,10,12,13)(11,14,15,16)(17,18,20,24,22,25,31,21)(19,26,30,32,29,23,27,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(1,3,4,7)(2,5,6,8)(10,13)(14,16)(17,19)(18,23)(20,30)(21,32)(22,29)(24,28)(25,26)(27,31);(2,6)(5,8)(9,11,12,15)(10,14,13,16)(17,20,22,31)(18,24,25,21)(19,27,29,30)(23,32,26,28);(17,21,31,25,22,24,20,18)(19,28,27,23,29,32,30,26)4028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 14666);