Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#13393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C2×C53×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
412 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(5,6)(7,19)(8,23)(9,17)(10,26)(11,15)(12,18)(13,20)(14,24)(16,25)(21,31)(22,32)(27,33)(28,30)(29,35)(34,36)(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);(1,2)(3,4)(5,7)(6,13)(8,9)(10,27)(11,20)(12,22)(14,26)(15,32)(16,33)(17,19)(18,23)(21,29)(24,28)(25,36)(30,31)(34,35);(2,4)(5,8,9,7,12,20,11,22)(6,14,15,33,18,34,17,31)(10,21,25,36,29,27,28,24)(13,30,19,35,23,16,32,26)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6381);