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×#33846 |
| 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 | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(3,4)(5,6,10,14)(7,15,19,33)(8,20,23,36)(9,24,22,12)(11,26,28,17)(13,30,32,21)(16,29,34,27)(18,35,25,31)(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)(6,11)(8,16)(9,25)(10,19)(12,29)(13,31)(14,28)(15,20)(17,21)(18,22)(23,34)(24,27)(26,30)(32,35)(33,36);(2,4);(6,12)(7,16)(8,21)(9,22)(11,15)(13,32)(14,24)(17,18)(19,34)(23,30)(25,26)(27,35)(28,33)(29,31)2915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26834);