Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#33460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator | C8 | C23×C4×C53 |
| Frattini, cosocle | C2×C8 | C24×C53 |
| prime radical | C2×C53×#508 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ #117×C53 ◁ C53×#405 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,4,3)(5,6,11,17)(7,15,9,21)(8,14,12,28)(10,24,26,30)(13,23,31,19)(16,20,35,27)(18,34,22,33)(25,29,36,32)(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);(5,7,11,9)(6,13,17,31)(8,18,12,22)(10,25,26,36)(14,29,28,32)(15,30,21,24)(16,33,35,34)(19,20,23,27);(1,3,4,2)(5,8,11,12)(6,14,17,28)(7,18,9,22)(10,20,26,27)(13,29,31,32)(15,34,21,33)(16,24,35,30)(19,25,23,36);(5,9,11,7)(6,15,17,21)(8,18,12,22)(10,23,26,19)(13,30,31,24)(14,33,28,34)(16,29,35,32)(20,25,27,36)3392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26448);