Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61674 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C53×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C53×#532 ◁ G | |
2032 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)(9,10,14,19)(11,15,20,29)(12,17,24,33)(13,16,26,18)(21,28,23,32)(22,30,35,27)(25,31,38,34)(36,40,37,39)(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)(10,15)(12,23)(13,22)(14,20)(16,30)(17,32)(18,27)(19,29)(21,24)(25,37)(26,35)(28,33)(31,39)(34,40)(36,38);(10,16)(11,20)(13,26)(15,27)(17,31)(18,19)(21,23)(25,38)(28,39)(29,30)(32,40)(33,34);(3,8)(5,7)(12,24)(17,33)(21,23)(25,38)(28,32)(31,34)(36,37)(39,40);(2,6)(5,7)(9,12,14,24)(10,17,19,33)(11,21,20,23)(13,25,26,38)(15,28,29,32)(16,31,18,34)(22,36,35,37)(27,39,30,40)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54662);