Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#18969 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(3,11)(4,9)(5,8)(6,10)(7,13)(12,16)(14,15)(17,18,22,26)(19,27,30,40)(20,24,31,38)(21,33,35,25)(23,34,37,29)(28,41,42,48)(32,45,44,39)(36,46,47,43)(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);(1,3,6,14)(2,7,10,16)(4,12,5,13)(8,15,9,11)(17,19,22,30)(18,23,26,37)(20,28,31,42)(21,34,35,29)(24,36,38,47)(25,40,33,27)(32,46,44,43)(39,48,45,41);(2,8)(4,5)(7,15)(9,10)(11,16)(12,13)(17,20)(18,24)(19,28)(21,32)(22,31)(23,36)(25,39)(26,38)(27,41)(29,43)(30,42)(33,45)(34,46)(35,44)(37,47)(40,48);(1,4,6,5)(2,8,10,9)(3,12,14,13)(7,15,16,11)(20,31)(24,38)(28,42)(32,44)(36,47)(39,45)(41,48)(43,46)1961 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11957);