Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61683 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C53×#3497 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C53×#532 ◁ G | |
2012 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,7)(4,6)(5,8)(9,10,14,19)(11,20,15,16)(12,23,25,34)(13,26,28,18)(17,29,32,21)(22,30,27,33)(24,37,39,36)(31,35,40,38)(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);(1,3)(2,5)(4,8)(6,7)(9,11,14,15)(10,16,19,20)(12,21,25,29)(13,27,28,22)(17,23,32,34)(18,33,26,30)(24,38,39,35)(31,37,40,36);(9,12,14,25)(10,17,19,32)(11,21,15,29)(13,24,28,39)(16,23,20,34)(18,31,26,40)(22,35,27,38)(30,36,33,37);(3,8)(5,7)(13,28)(18,26)(22,27)(24,39)(30,33)(31,40)(35,38)(36,37);(2,6)(5,7)(9,13)(10,18)(11,22)(12,24)(14,28)(15,27)(16,30)(17,31)(19,26)(20,33)(21,35)(23,36)(25,39)(29,38)(32,40)(34,37)2597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54671);