Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#19938 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C2×D4×C53 | C2×D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C42×C53 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,6,9)(3,7,5,13)(4,11,12,15)(8,14,16,10)(17,18,23,26)(19,27,30,32)(20,25,22,21)(24,28,31,29)(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);(1,3,6,5)(2,7,9,13)(4,10,12,14)(8,15,16,11)(17,19,23,30)(18,24,26,31)(20,29,22,28)(21,27,25,32);(1,4,6,12)(2,8,9,16)(3,10,5,14)(7,15,13,11)(17,20,23,22)(18,25,26,21)(19,28,30,29)(24,27,31,32);(17,21)(18,20)(19,24)(22,26)(23,25)(27,28)(29,32)(30,31)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12926);