Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9263 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#9269 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #386 |
| commutator | C22×C4 | C22×C4×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C53×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
480 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,4,6,5,8,3,7)(10,14)(11,18)(12,15)(17,22)(19,20)(21,23)(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);(2,6)(3,4)(7,8)(9,10,15,22,13,17,12,14)(11,16,18,23,20,24,19,21);(2,6)(3,4)(7,8)(9,11)(10,16)(12,19)(13,20)(14,21)(15,18)(17,24)(22,23)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 2257);