Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C210 |
| direct product | C2×C53×#3028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C25×C53 |
| prime radical | C2×C53×#585 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G | |
4790 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);(56,57,61,65)(58,62,68,75)(59,63,70,77)(60,71,72,64)(66,78,80,73)(67,81,82,74)(69,83,84,76)(79,85,87,86);(56,58)(57,62)(59,66)(60,67)(61,68)(63,73)(64,74)(65,75)(69,79)(70,80)(71,81)(72,82)(76,85)(77,78)(83,86)(84,87);(56,59)(57,63)(58,66)(60,69)(61,70)(62,73)(64,76)(65,77)(67,79)(68,80)(71,83)(72,84)(74,85)(75,78)(81,86)(82,87);(56,60,61,72)(57,64,65,71)(58,67,68,82)(59,69,70,84)(62,74,75,81)(63,76,77,83)(66,79,80,87)(73,85,78,86)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53385);