Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61693 |
| 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 | |
2014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,7)(4,6)(5,8)(9,10,13,15)(11,19,21,32)(12,23,24,17)(14,27,26,18)(16,28,29,22)(20,34,35,33)(25,31,39,38)(30,36,37,40)(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)(10,15)(12,24)(16,29)(18,27)(19,32)(20,35)(25,39)(36,40);(9,11,13,21)(10,16,15,29)(12,20,24,35)(14,28,26,22)(17,30,23,37)(18,32,27,19)(25,40,39,36)(31,34,38,33);(3,8)(5,7)(12,24)(17,23)(20,35)(25,39)(30,37)(31,38)(33,34)(36,40);(2,6)(5,7)(9,12,13,24)(10,17,15,23)(11,20,21,35)(14,25,26,39)(16,30,29,37)(18,31,27,38)(19,33,32,34)(22,36,28,40)2597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54681);