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×#23891 |
| 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 | |
1622 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)(5,6,10,14)(7,16,19,28)(8,20,22,30)(9,15,25,13)(11,24,27,18)(12,23,29,21)(17,26,33,36)(31,34,35,32)(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)(6,11,14,27)(8,17,22,33)(9,24,25,18)(12,26,29,36)(13,28,15,16)(20,31,30,35)(21,34,23,32);(2,4)(5,6)(7,16)(8,12)(9,13)(10,14)(11,24)(15,25)(17,31)(18,27)(19,28)(20,21)(22,29)(23,30)(26,32)(33,35)(34,36);(5,8,10,22)(6,12,14,29)(7,17,19,33)(9,23,25,21)(11,26,27,36)(13,30,15,20)(16,31,28,35)(18,34,24,32)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 16879);