Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#24800 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C2×#135×C53 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
842 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)(7,13)(8,21)(9,24)(10,17)(11,16)(12,19)(14,25)(15,22)(18,33)(20,28)(23,27)(26,32)(29,34)(30,35)(31,36)(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);(5,7,10,19,11,8,22,20)(6,12,15,13,16,28,17,21)(9,18,25,34,26,23,36,35)(14,27,24,29,31,33,32,30);(2,4)(5,8)(6,13)(7,11)(9,18)(10,20)(12,17)(14,30)(15,28)(16,21)(19,22)(23,26)(24,27)(25,34)(29,31)(32,33)(35,36);(5,9,10,25,11,26,22,36)(6,14,15,24,16,31,17,32)(7,18,19,34,8,23,20,35)(12,27,13,29,28,33,21,30)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 17788);