Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C29 |
| direct product | C53×#61091 |
| 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 | |
2650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 89 points:
(1,2)(3,4)(5,6,12,16)(7,17,21,29)(8,14,11,9)(10,24,26,15)(13,18,28,20)(19,33,35,31)(22,23,25,30)(27,34,36,32)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(5,7,12,21)(6,13,16,28)(8,20,11,18)(9,17,14,29)(10,19,26,35)(15,27,24,36)(22,34,25,32)(23,31,30,33);(2,4)(5,8,12,11)(6,14,16,9)(7,18,21,20)(10,25,26,22)(13,17,28,29)(15,23,24,30)(19,34,35,32)(27,33,36,31);(5,9)(6,8)(7,13)(10,23)(11,16)(12,14)(15,22)(17,18)(19,27)(20,29)(21,28)(24,25)(26,30)(31,32)(33,34)(35,36);(5,10,12,26)(6,15,16,24)(7,19,21,35)(8,22,11,25)(9,23,14,30)(13,27,28,36)(17,31,29,33)(18,32,20,34)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54079);