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×#61086 |
| 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 | |
2666 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)(12,22)(13,24)(14,29)(15,26)(16,31)(17,23)(25,27)(28,30)(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);(5,6,10,12)(7,15,18,24)(8,14,19,27)(9,22,21,11)(13,23,26,17)(16,30,31,35)(20,29,33,25)(28,34,36,32);(2,4)(6,12)(8,19)(11,22)(13,26)(15,24)(16,31)(20,33)(32,34);(5,7,10,18)(6,13,12,26)(8,16,19,31)(9,23,21,17)(11,24,22,15)(14,28,27,36)(20,34,33,32)(25,35,29,30);(5,8)(6,14)(7,16)(9,20)(10,19)(11,25)(12,27)(13,28)(15,30)(17,32)(18,31)(21,33)(22,29)(23,34)(24,35)(26,36)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54074);