Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#13326 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C22×D16×C53 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ C2×C4×C8×C53 ◁ G | |
614 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)(10,14)(11,17)(13,19)(15,23)(16,24)(18,21)(20,22)(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);(2,4)(5,6)(7,8)(9,10,12,15)(11,18,20,24)(13,21,19,16)(14,22,23,17);(6,8)(9,10)(11,18)(12,15)(13,21)(14,17)(16,19)(20,24)(22,23)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6314);