Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#19817 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C53 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C42×C53 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10)(18,22)(20,28)(23,31)(24,29)(25,32)(26,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(17,18,21,24)(19,25,27,31)(20,29,28,22)(23,30,32,26);(1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9);(17,19,21,27)(18,23,24,32)(20,30,28,26)(22,31,29,25)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12805);