Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C82×C53 · Schur multiplier (H2) = C2×C42 |
| direct product | C53×#7014 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C53 | C42 |
| commutator | C4 | C82×C53 |
| Frattini, cosocle | C43 | C22×C53 |
| socle, prime radical | C23×C53 | #95 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C53 ◁ G | |
338 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 2 generators on 85 points:
(1,2,3,5,4,6,7,8)(17,18)(19,25,27,31)(20,23)(21,24)(22,26,29,32)(28,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(9,10,11,13,12,14,15,16)(17,19)(18,22,24,29)(20,26)(21,27)(23,25,30,31)(28,32)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 2);