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×#33835 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C4×D4×C53 ◁ C8×D4×C53 ◁ G | |
670 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)(5,6,12,17)(7,18,21,35)(8,14,11,27)(9,24,25,10)(13,29,32,20)(15,16,23,22)(19,34,28,33)(26,30,36,31)(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);(5,7,12,21)(6,13,17,32)(8,19,11,28)(9,18,25,35)(10,26,24,36)(14,30,27,31)(15,20,23,29)(16,33,22,34);(2,4)(5,8,12,11)(6,14,17,27)(7,19,21,28)(9,22,25,16)(10,23,24,15)(13,30,32,31)(18,34,35,33)(20,26,29,36);(5,9)(6,15)(7,13)(8,22)(10,14)(11,16)(12,25)(17,23)(18,26)(19,30)(20,33)(21,32)(24,27)(28,31)(29,34)(35,36)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26823);