Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#19063 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
806 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 101 points:
(3,9)(4,11)(6,14)(7,12)(10,13)(15,16)(17,18)(19,28)(20,25)(21,26)(22,35)(23,27)(24,30)(29,44)(31,38)(32,40)(33,42)(34,41)(36,39)(37,45)(43,46)(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);(1,2,5,8)(3,6,10,15)(4,12,11,7)(9,16,13,14)(17,19,23,31)(18,24,27,39)(20,29,34,46)(21,30,22,36)(25,37,41,48)(26,38,35,28)(32,45,33,47)(40,43,42,44);(1,3)(2,6)(4,13)(5,10)(7,16)(8,15)(9,11)(12,14)(17,20,23,34)(18,25,27,41)(19,29,31,46)(21,33,22,32)(24,37,39,48)(26,42,35,40)(28,43,38,44)(30,47,36,45);(17,21,23,22)(18,26,27,35)(19,30,31,36)(20,32,34,33)(24,38,39,28)(25,40,41,42)(29,45,46,47)(37,43,48,44)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12051);