Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61290 |
| 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 | |
1774 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2,5,4)(3,7,8,6)(9,10,14,19)(11,15,22,31)(12,23,25,17)(13,16,27,18)(20,33,24,29)(21,28,36,30)(26,34,38,32)(35,40,37,39)(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)(2,6)(4,7)(5,8)(9,11,14,22)(10,15,19,31)(12,24,25,20)(13,21,27,36)(16,28,18,30)(17,33,23,29)(26,37,38,35)(32,40,34,39);(1,4,5,2)(3,7,8,6)(10,16)(13,27)(15,28)(17,32)(18,19)(21,36)(23,34)(26,38)(29,39)(30,31)(33,40)(35,37);(3,8)(6,7)(12,25)(17,23)(20,24)(26,38)(29,33)(32,34)(35,37)(39,40);(9,12,14,25)(10,17,19,23)(11,20,22,24)(13,26,27,38)(15,29,31,33)(16,32,18,34)(21,35,36,37)(28,39,30,40)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54278);