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×#25438 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C53×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
892 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,3,4)(5,6,11,17)(7,14,8,20)(9,23,25,36)(10,27,12,16)(13,22,29,19)(15,26,32,24)(18,33,21,28)(30,35,31,34)(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)(5,7,12,22,11,8,10,19)(6,13,27,20,17,29,16,14)(9,18,26,35,25,21,24,34)(15,28,36,31,32,33,23,30);(1,2)(3,4)(5,8)(6,14)(7,11)(9,18)(10,22)(12,19)(13,27)(15,31)(16,29)(17,20)(21,25)(23,28)(24,34)(26,35)(30,32)(33,36);(5,9,12,26,11,25,10,24)(6,15,27,36,17,32,16,23)(7,18,22,35,8,21,19,34)(13,28,20,31,29,33,14,30)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 18426);