Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C53 · Schur multiplier (H2) = C4 |
| direct product | C53×#7053 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C53 | C42 |
| commutator | C4 | C4×C16×C53 |
| Frattini, cosocle | C82 | C22×C53 |
| socle, prime radical | C22×C53 | #322 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42×C53 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 2 generators on 85 points:
(17,18,19,23,20,25,27,31,21,24,26,32,28,22,29,30)(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);(1,2,3,6,4,7,9,12,5,8,10,13,11,14,15,16)(18,22,24,25)(19,26)(23,31,32,30)(27,29)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 41);