Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#19095 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3568 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
834 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 101 points:
(3,10)(4,5)(7,14)(8,12)(11,13)(15,16)(17,18,23,28)(19,29,33,38)(20,25,35,41)(21,27,22,26)(24,31,39,32)(30,44,46,43)(34,42,36,40)(37,47,48,45)(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)(3,7)(4,8)(5,12)(6,9)(10,15)(11,16)(13,14)(17,19)(18,24)(20,30)(21,32)(22,31)(23,33)(25,37)(26,29)(27,38)(28,39)(34,47)(35,46)(36,45)(40,43)(41,48)(42,44);(1,3)(2,7)(4,10)(5,13)(6,11)(8,15)(9,16)(12,14)(17,20)(18,25)(19,30)(21,34)(22,36)(23,35)(24,37)(26,40)(27,42)(28,41)(29,43)(31,45)(32,47)(33,46)(38,44)(39,48);(1,4,6,5)(2,8,9,12)(3,10,11,13)(7,15,16,14)(17,21,23,22)(18,26,28,27)(19,31,33,32)(20,34,35,36)(24,38,39,29)(25,40,41,42)(30,45,46,47)(37,44,48,43)1643 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12083);