Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#26082 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C2×#41×C53 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,22)(12,17)(13,28)(14,20)(15,21)(16,24)(18,29)(19,26)(23,37)(25,32)(27,31)(30,34)(33,39)(35,40)(36,38)(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);(9,11,14,24,15,12,26,25)(10,16,19,22,21,32,20,17)(13,23,29,38,30,27,40,39)(18,31,28,36,35,37,34,33);(1,3,4,8)(2,5,6,7)(9,12)(10,17)(11,15)(13,27)(14,25)(16,19)(18,33)(20,32)(21,22)(23,30)(24,26)(28,31)(29,39)(34,37)(35,36)(38,40);(9,13,26,40,15,30,14,29)(10,18,20,34,21,35,19,28)(11,23,25,39,12,27,24,38)(16,31,17,33,32,37,22,36)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 19070);