Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C53×#1718 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C53 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 13568 |
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);(56,57,60,63)(58,64,65,71)(59,67,68,62)(61,69,70,66)(72,73)(74,80)(75,77)(76,84)(78,82)(79,83)(81,86)(85,87);(56,58,59,66,60,65,68,69)(57,61,62,64,63,70,67,71)(73,77)(78,85)(79,84)(80,86);(58,65)(61,70)(64,71)(66,69)(72,74,76,82,75,81,83,87)(73,78,79,80,77,85,84,86)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12598);