Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#25987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C2×2−1+4×C53 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,21)(12,22)(13,16)(14,20)(15,19)(17,23)(18,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(9,11,15,17)(10,12,19,13)(14,16,24,22)(18,23,20,21);(1,3,4,8)(2,5,6,7)(9,12,15,13)(10,16,19,22)(11,20,17,18)(14,21,24,23);(9,13,15,12)(10,17,19,11)(14,21,24,23)(16,18,22,20)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 18975);