Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#19013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3531 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 101 points:
(2,6)(4,11)(7,13)(8,12)(9,15)(14,16)(17,18,23,28)(19,29,32,41)(20,25,34,40)(21,27,22,26)(24,35,38,31)(30,44,47,43)(33,42,36,39)(37,45,48,46)(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);(4,11)(6,12)(9,15)(13,16)(17,19,23,32)(18,24,28,38)(20,30,34,47)(21,31,22,35)(25,37,40,48)(26,29,27,41)(33,45,36,46)(39,43,42,44);(1,2)(3,7)(4,12)(5,8)(6,11)(9,16)(10,14)(13,15)(17,20)(18,25)(19,30)(21,33)(22,36)(23,34)(24,37)(26,39)(27,42)(28,40)(29,43)(31,45)(32,47)(35,46)(38,48)(41,44);(1,3,5,10)(2,7,8,14)(4,9,11,15)(6,13,12,16)(17,21,23,22)(18,26,28,27)(19,31,32,35)(20,33,34,36)(24,29,38,41)(25,39,40,42)(30,45,47,46)(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, 12001);