Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#13332 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C2×C53×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×C4×C8×C53 ◁ G | |
566 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)(7,19)(8,25)(9,14)(10,17)(11,30)(12,18)(13,21)(15,27)(16,28)(20,35)(22,34)(23,31)(24,32)(26,36)(29,33)(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);(2,4)(5,7,12,24)(6,13,18,34)(8,26,9,29)(10,20,11,23)(14,32,25,19)(15,31,16,35)(17,36,30,33)(21,28,22,27);(6,14)(7,20)(8,27)(9,28)(10,11)(13,31)(15,30)(16,17)(18,25)(19,33)(21,22)(23,24)(32,36)(34,35)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6320);