Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C26 |
| direct product | C53×#33527 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×#41×C53 ◁ C2×#131×C53 ◁ G | |
1098 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(3,4)(6,11)(8,18)(9,20)(12,24)(13,28)(14,25)(16,31)(17,30)(19,22)(21,23)(26,35)(27,36)(29,34)(32,33)(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)(7,12,15,26)(8,19,21,28)(9,22,20,13)(11,23,25,18)(16,32,29,36)(17,33,30,27)(24,34,35,31);(2,4)(7,15)(12,26)(16,29)(17,30)(24,35)(27,33)(31,34)(32,36);(5,7,10,15)(6,12,14,26)(8,16,21,29)(9,17,20,30)(11,24,25,35)(13,27,22,33)(18,31,23,34)(19,32,28,36)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26515);