Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C53×#532 ◁ G | |
2046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,7)(4,6)(5,8)(9,10,13,18)(11,20,22,15)(12,24,26,17)(14,16,28,19)(21,30,25,33)(23,31,36,29)(27,34,38,32)(35,39,37,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3)(2,5)(4,8)(6,7)(9,11,13,22)(10,15,18,20)(12,25,26,21)(14,23,28,36)(16,29,19,31)(17,33,24,30)(27,37,38,35)(32,40,34,39);(10,16)(14,28)(15,29)(17,32)(18,19)(20,31)(23,36)(24,34)(27,38)(30,39)(33,40)(35,37);(3,8)(5,7)(12,26)(17,24)(21,25)(27,38)(30,33)(32,34)(35,37)(39,40);(2,6)(5,7)(9,12,13,26)(10,17,18,24)(11,21,22,25)(14,27,28,38)(15,30,20,33)(16,32,19,34)(23,35,36,37)(29,39,31,40)2597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54679);