Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C22 |
| direct product | C53×#10375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C53 |
| prime radical | C24×C53 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 77 points:
(2,5)(3,7)(6,8)(9,10)(11,14)(12,19,21,15)(13,16)(17,24,20,22)(18,23)(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);(9,11)(10,14)(12,20,21,17)(13,18)(15,22,19,24)(16,23);(1,2,4,6)(3,8,7,5)(9,12,13,21)(10,15,16,19)(11,17,18,20)(14,22,23,24)1961 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 3363);