Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#11062 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #121 |
| commutator | C22×C4 | C22×C4×C53 |
| Frattini, cosocle | C23×C4 | C23×C53 |
| prime radical | C24×C53 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C23×C4×C53 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4)(6,8)(9,10,15,17,13,18,14,19)(11,12,16,23,20,21,24,22)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(5,6,7,8)(9,11)(10,12)(13,20)(14,24)(15,16)(17,23)(18,21)(19,22);(9,12,13,21)(10,16,18,24)(11,19,20,17)(14,23,15,22)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 4050);