Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#60720 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C53×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C4×#41×C53 ◁ G | |
1846 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)(3,6)(4,5)(7,8)(9,10,14,18)(11,19,20,32)(12,16,23,30)(13,25,26,17)(15,27,28,22)(21,33,34,40)(24,37,36,31)(29,38,39,35)(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);(2,5)(6,8)(11,20)(12,23)(15,28)(16,30)(19,32)(22,27)(24,36)(31,37);(9,11,13,22,14,20,26,27)(10,15,17,19,18,28,25,32)(12,21,24,35,23,34,36,38)(16,29,31,33,30,39,37,40);(1,3,4,7)(2,6,5,8)(12,23)(16,30)(21,34)(24,36)(29,39)(31,37)(33,40)(35,38);(9,12)(10,16)(11,21)(13,24)(14,23)(15,29)(17,31)(18,30)(19,33)(20,34)(22,35)(25,37)(26,36)(27,38)(28,39)(32,40)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53708);