Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#33850 |
| 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 ◁ C4×D4×C53 ◁ C8×D4×C53 ◁ G | |
686 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)(5,6,11,17)(7,18,23,36)(8,13,26,16)(9,25,15,33)(10,24,14,28)(12,30,32,21)(19,35,22,27)(20,34,31,29)(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);(5,7,11,23)(6,12,17,32)(8,19,26,22)(9,27,15,35)(10,29,14,34)(13,31,16,20)(18,28,36,24)(21,33,30,25);(2,4)(5,8,11,26)(6,13,17,16)(7,19,23,22)(9,24,15,28)(10,25,14,33)(12,31,32,20)(18,35,36,27)(21,34,30,29);(5,9)(6,14)(7,20)(8,24)(10,17)(11,15)(12,19)(13,33)(16,25)(18,21)(22,32)(23,31)(26,28)(27,29)(30,36)(34,35)2915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26838);