Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C2×C53×#2399 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C53 | C23 |
| commutator, Frattini, cosocle | C23 | C25×C53 |
| socle, prime radical | C24×C53 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C53 ◁ G | |
2814 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 5 generators on 75 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);(60,61)(62,65)(63,64)(66,67)(68,69,72,75)(70,74,71,73);(56,57)(58,59)(68,70,72,71)(69,73,75,74);(57,59)(61,64)(65,67)(68,70,72,71)(69,74,75,73);(60,62,63,66)(61,65,64,67)(68,71,72,70)(69,73,75,74)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 27534);