Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#33653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| prime radical | C53×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×#41×C53 ◁ C2×#131×C53 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,6)(4,5)(7,8)(9,10,14,19)(11,16,20,30)(12,15,25,29)(13,26,24,18)(17,33,28,23)(21,27,34,38)(22,37,35,32)(31,40,39,36)(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);(2,5)(6,8)(11,20)(16,30)(21,34)(22,35)(27,38)(31,39)(32,37)(36,40);(1,3,4,7)(2,6,5,8)(10,15)(12,23)(13,24)(16,27)(17,18)(19,29)(21,36)(22,35)(25,33)(26,28)(30,38)(31,32)(34,40)(37,39);(9,11,14,20)(10,16,19,30)(12,21,25,34)(13,22,24,35)(15,27,29,38)(17,31,28,39)(18,32,26,37)(23,36,33,40)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26641);