Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#60724 |
| 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 ◁ C4×#41×C53 ◁ G | |
1874 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)(11,16)(12,22)(13,18)(14,29)(15,19)(17,24)(20,32)(21,30)(23,38)(25,39)(26,33)(27,40)(28,35)(31,37)(34,36)(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)(9,11,15,14)(10,16,19,29)(12,20,25,24)(13,26,28,21)(17,22,32,39)(18,33,35,30)(23,37,27,36)(31,40,34,38);(9,12,14,24,15,25,11,20)(10,17,16,22,19,32,29,39)(13,27,26,36,28,23,21,37)(18,34,30,40,35,31,33,38);(1,3,4,7)(2,6,5,8)(13,28)(18,35)(21,26)(23,27)(30,33)(31,34)(36,37)(38,40);(9,13)(10,18)(11,21)(12,23)(14,26)(15,28)(16,30)(17,31)(19,35)(20,36)(22,38)(24,37)(25,27)(29,33)(32,34)(39,40)3392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53712);