Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C53 · Schur multiplier (H2) = C213 |
| direct product | C2×C53×#3461 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C53 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C53 |
| socle | C23×C53 | C25 |
| prime radical | C2×C53×#537 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C53 ◁ G | |
7130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 6 generators on 79 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)(54,55);(56,57)(58,61)(59,60)(62,63)(64,65)(66,72)(67,70)(68,71)(69,74)(73,78)(75,77)(76,79);(64,66,68,74)(65,69,71,72)(67,75,76,73)(70,78,79,77);(57,60)(61,63)(64,67,68,76)(65,70,71,79)(66,73,74,75)(69,77,72,78);(65,71)(69,72)(70,79)(77,78);(56,58,59,62)(57,61,60,63)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 55670);