Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C2×C53×#1638 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C22×D4×C53 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6784 |
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);(56,57,61,64)(58,65,67,70)(59,63,60,68)(62,69,71,66)(72,73,77,81)(74,82,85,86)(75,80,76,79)(78,84,87,83);(56,58)(57,62)(59,66)(60,69)(61,67)(63,70)(64,71)(65,68)(72,74,77,85)(73,78,81,87)(75,84,76,83)(79,86,80,82);(56,59,61,60)(57,63,64,68)(58,66,67,69)(62,70,71,65)(73,79)(75,76)(78,86)(80,81)(82,87)(83,84)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11481);