Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×#7459 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C53 | D8 |
| commutator | C8 | C2×C16×C53 |
| Frattini, cosocle | C4×C16 | C22×C53 |
| socle | C2×C53 | #1370 |
| prime radical | C22×C53 | #364 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C53 ◁ C2×C16×C53 ◁ C4×C16×C53 ◁ G | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 2 generators on 85 points:
(1,2,5,12,7,14,3,16,8,13,20,29,17,11,21,30,9,15,25,31,4,23,22,32,6,26,18,10,24,27,19,28)(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);(1,3,17,25,6,19,7,20,9,22,24,5,8,21,4,18)(2,10,23,30,13,12,27,32,15,29,14,28,26,31,11,16)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 447);