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×#25437 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C2×AGL(1,ℤ/8)×C53 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
894 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)(7,14)(8,20)(9,23)(10,27)(11,17)(12,16)(13,19)(15,24)(18,33)(21,28)(22,29)(25,36)(26,32)(30,34)(31,35)(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);(5,9,10,24,11,25,12,26)(6,15,16,23,17,32,27,36)(7,18,19,34,8,21,22,35)(13,28,14,30,29,33,20,31)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 18425);