Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C23×C4 |
| direct product | C53×#33703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| prime radical | C2×#135×C53 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ #117×C53 ◁ C53×#405 ◁ G | |
570 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)(3,5)(4,6)(7,8)(9,10,16,20)(11,21,23,37)(12,13,27,30)(14,31,29,18)(15,32,28,19)(17,33,34,24)(22,40,39,26)(25,35,36,38)(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);(1,3,4,7)(2,5,6,8)(9,11,14,25,15,26,13,24,16,23,29,36,28,40,30,33)(10,17,12,22,19,35,18,21,20,34,27,39,32,38,31,37);(2,6)(5,8)(9,12,13,20,28,31,14,19,16,27,30,10,15,18,29,32)(11,22,24,34,40,37,25,35,23,39,33,17,26,21,36,38);(11,23)(17,34)(21,37)(22,39)(24,33)(25,36)(26,40)(35,38)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26691);