Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#18996 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3529 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
948 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,5)(3,7)(6,8)(9,10,15,20)(11,21,24,33)(12,17,26,32)(13,19,14,18)(16,27,30,23)(22,36,39,35)(25,34,28,31)(29,37,40,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(3,7)(5,8)(9,11)(10,16)(12,22)(13,23)(14,27)(15,24)(17,29)(18,21)(19,33)(20,30)(25,37)(26,39)(28,38)(31,35)(32,40)(34,36);(1,2)(3,8)(4,6)(5,7)(9,12)(10,17)(11,22)(13,25)(14,28)(15,26)(16,29)(18,31)(19,34)(20,32)(21,35)(23,37)(24,39)(27,38)(30,40)(33,36);(9,13,15,14)(10,18,20,19)(11,23,24,27)(12,25,26,28)(16,21,30,33)(17,31,32,34)(22,37,39,38)(29,35,40,36)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11984);