Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18562 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#18592 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C2×#41×C53 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
860 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)(3,10)(4,8)(5,14)(6,9)(7,11)(12,16)(13,15)(17,18,24,21)(19,28,20,31)(22,27,23,26)(25,30,32,29)(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)(2,7)(4,11)(5,12)(6,13)(8,15)(9,16)(10,14)(17,19,24,20)(18,25,21,32)(22,30,23,29)(26,31,27,28);(1,4,6,5)(2,8,9,14)(3,11,13,12)(7,15,16,10)(17,20,24,19)(18,25,21,32)(22,29,23,30)(26,31,27,28);(1,4,6,5)(2,8,9,14)(3,12,13,11)(7,10,16,15)(17,21,24,18)(19,25,20,32)(22,27,23,26)(28,30,31,29)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11580);