Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C29 |
| direct product | C53×#61083 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C53×#532 ◁ G | |
2674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 89 points:
(1,2)(3,4)(5,6,10,14)(7,15,19,25)(8,20,21,12)(9,23,24,13)(11,16,27,18)(17,31,32,29)(22,28,36,35)(26,33,34,30)(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)(8,17,21,32)(9,16,24,18)(12,26,20,34)(13,25,23,15)(22,30,36,33)(28,31,35,29);(2,4)(8,21)(12,20)(17,32)(22,36)(26,34)(28,35)(29,31)(30,33);(7,16)(9,24)(11,25)(13,23)(15,27)(17,30)(18,19)(22,36)(26,31)(28,35)(29,34)(32,33);(5,8,10,21)(6,12,14,20)(7,17,19,32)(9,22,24,36)(11,26,27,34)(13,28,23,35)(15,29,25,31)(16,30,18,33)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54071);