Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#33844 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| prime radical | C53×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C4×D4×C53 ◁ C8×D4×C53 ◁ 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)(3,4)(5,6,11,15)(7,16,17,35)(8,21,25,28)(9,24,13,30)(10,23,27,14)(12,31,32,19)(18,26,34,33)(20,36,29,22)(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);(5,7,11,17)(6,12,15,32)(8,22,25,36)(9,26,13,33)(10,29,27,20)(14,34,23,18)(16,30,35,24)(19,21,31,28);(2,4)(7,17)(12,32)(16,35)(18,34)(19,31)(20,29)(22,36)(26,33);(5,8,11,25)(6,13,15,9)(7,18,17,34)(10,30,27,24)(12,29,32,20)(14,28,23,21)(16,19,35,31)(22,33,36,26)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26832);