Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#25194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C53×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
980 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(5,6,10,15,11,17,9,16)(7,18,20,12,22,29,21,13)(8,23,25,14,27,31,26,32)(19,28,35,36,24,30,34,33)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(1,2)(3,4)(5,7,10,20,11,22,9,21)(6,12,15,29,17,13,16,18)(8,24,25,34,27,19,26,35)(14,30,31,33,32,28,23,36);(2,4)(5,7,11,22)(6,13,17,12)(8,19,27,24)(9,20,10,21)(14,30,32,28)(15,29,16,18)(23,33,31,36)(25,34,26,35);(5,8)(6,14)(7,19)(9,26)(10,25)(11,27)(12,28)(13,30)(15,31)(16,23)(17,32)(18,33)(20,35)(21,34)(22,24)(29,36)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 18182);