Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13396 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#13396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C53×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(3,12)(4,16)(5,18)(7,21)(8,24)(9,10)(13,30)(14,28)(15,17)(19,31)(20,29)(22,32)(23,25)(26,27)(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)(3,13)(4,8)(5,10)(6,11)(7,15)(9,18)(12,25)(14,23)(16,24)(17,32)(19,27)(20,22)(21,29)(26,31)(28,30);(1,3,5,20,6,14,18,15)(2,7,10,13,11,22,9,23)(4,17,16,28,19,29,31,12)(8,25,24,32,27,30,26,21)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6384);