Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#26925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C23×C53 | H(5,𝔽2) |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,5)(3,7,8,6)(9,10,13,18,15,20,14,19)(11,21,23,32,25,31,24,16)(12,26,27,34,29,33,28,17)(22,30,36,39,38,40,37,35)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(2,5)(6,7)(9,11,15,25)(10,16,20,32)(12,22,29,38)(13,24,14,23)(17,30,34,40)(18,31,19,21)(26,35,33,39)(27,37,28,36);(9,10,15,20)(11,21,25,31)(12,17,29,34)(13,19,14,18)(16,24,32,23)(22,35,38,39)(26,27,33,28)(30,36,40,37);(1,3,4,8)(2,6,5,7)(9,12)(10,17)(11,22)(13,28)(14,27)(15,29)(16,30)(18,33)(19,26)(20,34)(21,35)(23,37)(24,36)(25,38)(31,39)(32,40)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 19913);