Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#26848 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C53×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,22)(12,27)(13,29)(14,32)(15,20)(16,21)(17,25)(18,24)(19,23)(26,37)(28,40)(30,35)(31,39)(33,38)(34,36)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(9,11,14,25,16,26,15,33)(10,17,20,22,21,38,32,37)(12,13,24,23,28,31,34,30)(18,39,27,19,36,29,40,35);(2,5)(6,8)(9,12,14,24,16,28,15,34)(10,18,20,27,21,36,32,40)(11,23,25,31,26,30,33,13)(17,35,22,39,38,19,37,29);(1,3,4,7)(2,6,5,8)(9,13,14,23,16,31,15,30)(10,19,20,29,21,35,32,39)(11,24,25,28,26,34,33,12)(17,36,22,40,38,18,37,27)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 19836);