Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C53 · Schur multiplier (H2) = C210 |
| direct product | C2×C53×#2889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C53 |
| Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C22×2−1+4×C53 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×#41×C53 ◁ G | |
4770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 87 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)(54,55);(56,57,60,65,61,64,73,78)(58,66,68,79,69,62,72,75)(59,63,71,77,70,76,83,86)(67,80,82,87,81,74,84,85);(56,58,61,69)(57,62,64,66)(59,67,70,81)(60,72,73,68)(63,74,76,80)(65,79,78,75)(71,84,83,82)(77,87,86,85);(56,59)(57,63)(58,67)(60,71)(61,70)(62,74)(64,76)(65,77)(66,80)(68,82)(69,81)(72,84)(73,83)(75,85)(78,86)(79,87);(59,70)(63,76)(67,81)(71,83)(74,80)(77,86)(82,84)(85,87)4346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53063);