Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#25191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C53×#3012 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(5,6,11,15,12,17,10,16)(7,18,21,13,23,31,22,32)(8,24,26,33,9,28,27,14)(19,35,20,30,36,29,25,34)(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);(1,2)(3,4)(5,7,11,21,12,23,10,22)(6,13,15,31,17,32,16,18)(8,25,26,19,9,20,27,36)(14,30,24,29,33,34,28,35);(2,4)(5,8,12,9)(6,14,17,33)(7,19,23,36)(10,26,11,27)(13,29,32,35)(15,28,16,24)(18,34,31,30)(20,21,25,22);(5,9,12,8)(6,14,17,33)(7,20,23,25)(10,26,11,27)(13,30,32,34)(15,24,16,28)(18,35,31,29)(19,21,36,22)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 18179);