Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C26 |
| direct product | C2×C53×#1868 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C53 | #120 |
| commutator | C23 | C23×C4×C53 |
| Frattini, cosocle | C22×C4 | C24×C53 |
| socle | C22×C53 | #385 |
| prime radical | C22×#41×C53 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C53 ◁ C23×C4×C53 ◁ G | |
1342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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);(56,57,60,64,61,65,71,77)(58,62,68,74,67,73,81,85)(59,63,70,76,69,75,82,86)(66,78,80,87,79,72,83,84);(56,58,60,68,61,67,71,81)(57,62,64,74,65,73,77,85)(59,66,70,80,69,79,82,83)(63,72,76,84,75,78,86,87);(56,59)(57,63)(58,66)(60,70)(61,69)(62,72)(64,76)(65,75)(67,79)(68,80)(71,82)(73,78)(74,84)(77,86)(81,83)(85,87)3392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 13879);