Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C27 |
| direct product | C53×#23889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
1648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(3,4)(5,6)(7,17)(8,13)(9,25)(10,15)(11,16)(12,20)(14,23)(18,33)(19,27)(21,28)(22,32)(24,31)(26,30)(29,34)(35,36)(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);(5,7,11,22)(6,12,16,28)(8,19,24,35)(9,21,10,20)(13,29,31,33)(14,27,30,36)(15,32,25,17)(18,26,34,23);(2,4)(5,8)(6,13)(7,18)(9,23)(10,26)(11,24)(12,27)(14,25)(15,30)(16,31)(17,33)(19,20)(21,35)(22,34)(28,36)(29,32);(5,8)(6,14)(7,19)(9,26)(10,23)(11,24)(12,27)(13,25)(15,31)(16,30)(17,29)(18,20)(21,34)(22,35)(28,36)(32,33)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 16877);