Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C29 |
| direct product | C53×#61081 |
| 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 | |
2658 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)(6,11)(8,19)(9,21)(12,24)(13,28)(14,22)(15,27)(16,31)(17,23)(25,29)(26,30)(35,36)(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);(5,6,10,14)(7,15,18,24)(8,13,19,29)(9,22,21,11)(12,23,27,17)(16,30,31,35)(20,28,33,25)(26,34,36,32);(2,4)(8,19)(13,29)(16,31)(20,33)(25,28)(26,36)(30,35)(32,34);(5,7,10,18)(6,12,14,27)(8,16,19,31)(9,23,21,17)(11,24,22,15)(13,26,29,36)(20,34,33,32)(25,35,28,30);(5,8)(6,13)(7,16)(9,20)(10,19)(11,25)(12,26)(14,29)(15,30)(17,32)(18,31)(21,33)(22,28)(23,34)(24,35)(27,36)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54069);