Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13391 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#13391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2033 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C53×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2)(3,15)(4,19)(5,13)(6,22)(7,11)(8,14)(9,16)(10,20)(12,24)(17,31)(18,29)(21,30)(23,26)(25,27)(28,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(1,3)(2,9)(4,5)(6,17)(7,16)(8,18)(10,27)(11,29)(12,26)(13,15)(14,19)(20,21)(22,28)(23,25)(24,32)(30,31);(1,4,5,3,8,16,7,18)(2,10,11,26,14,28,13,31)(6,23,21,20,25,17,24,32)(9,12,15,27,19,30,29,22)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6379);