Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61207 |
| 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 | |
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:
(1,2,4,6)(3,7,8,5)(9,10)(11,15)(12,17)(13,16)(14,19)(18,26)(20,28)(21,27)(22,30)(23,32)(24,33)(25,31)(29,36)(34,38)(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)(9,11,14,22)(10,15,19,30)(12,23,24,20)(13,21,26,36)(16,27,18,29)(17,32,33,28)(25,37,38,35)(31,40,34,39);(10,16)(13,26)(15,27)(17,31)(18,19)(21,36)(25,38)(28,39)(29,30)(32,40)(33,34)(35,37);(3,8)(5,7)(12,24)(17,33)(20,23)(25,38)(28,32)(31,34)(35,37)(39,40);(9,12,14,24)(10,17,19,33)(11,20,22,23)(13,25,26,38)(15,28,30,32)(16,31,18,34)(21,35,36,37)(27,39,29,40)2915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54195);