Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#13314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C2×C53×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(1,2)(3,4)(5,6,11,17)(7,18,21,32)(8,12,24,28)(9,16,10,15)(13,25,31,19)(14,23,27,22)(20,29,34,30)(26,35,36,33)(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);(6,12)(7,19)(8,22)(9,10)(13,29)(14,16)(15,27)(17,28)(18,26)(20,34)(21,25)(23,24)(30,31)(32,36);(2,4)(5,7)(6,13)(8,20)(9,25)(10,19)(11,21)(12,26)(14,30)(15,32)(16,18)(17,31)(22,33)(23,35)(24,34)(27,29)(28,36)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6302);