Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13398 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C22 |
| direct product | C53×#13501 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #481 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C24×C53 | SD16 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C22×M16×C53 ◁ G | |
302 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 73 points:
(5,6,10,17,16,20,7,13,9,11,18,12,8,14,15,19)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(1,2)(3,4)(6,11)(7,15)(10,18)(14,20);(2,4)(6,12,11,17)(7,10)(8,16)(13,14,19,20)(15,18)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6489);