Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#19071 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3553 | 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)(17,18,23,27)(19,28,31,38)(20,25,34,41)(21,26,22,35)(24,36,39,30)(29,44,46,43)(32,40,33,42)(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);(4,11)(6,12)(9,15)(13,16)(17,19)(18,24)(20,29)(21,30)(22,36)(23,31)(25,37)(26,38)(27,39)(28,35)(32,45)(33,47)(34,46)(40,43)(41,48)(42,44);(1,2)(3,7)(4,12)(5,8)(6,11)(9,16)(10,14)(13,15)(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);(1,3,5,10)(2,7,8,14)(4,9,11,15)(6,13,12,16)(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, 12059);