Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#19054 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3150 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,5)(3,7)(6,8)(9,10)(11,20)(12,17)(13,18)(14,27)(15,19)(16,22)(21,36)(23,30)(24,32)(25,34)(26,33)(28,31)(29,37)(35,38)(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);(3,7)(5,8)(9,11)(10,16)(12,21)(13,22)(14,28)(15,23)(17,29)(18,30)(19,31)(20,27)(24,37)(25,39)(26,38)(32,35)(33,40)(34,36);(1,2)(3,8)(4,6)(5,7)(9,12,15,26)(10,17,19,33)(11,21,23,38)(13,25,14,24)(16,29,31,40)(18,34,27,32)(20,35,30,36)(22,39,28,37);(9,13,15,14)(10,18,19,27)(11,22,23,28)(12,24,26,25)(16,30,31,20)(17,32,33,34)(21,37,38,39)(29,35,40,36)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12042);