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) = C24 |
| direct product | C53×#33905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| prime radical | C2×D4×C53 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C4×D4×C53 ◁ C8×D4×C53 ◁ G | |
484 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,5,4)(3,7,8,6)(9,10)(11,20)(12,17)(13,16)(14,27)(15,21)(18,26)(19,25)(22,33)(23,30)(24,31)(28,36)(29,40)(32,39)(34,38)(35,37)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3)(2,6)(4,7)(5,8)(9,11)(10,15)(12,21)(13,22)(14,23)(16,28)(17,20)(18,29)(19,30)(24,36)(25,37)(26,38)(27,35)(31,33)(32,34)(39,40);(1,4,5,2)(3,7,8,6)(10,16)(13,26)(14,25)(15,28)(17,31)(18,19)(20,33)(22,38)(23,37)(24,39)(27,32)(29,30)(34,35)(36,40);(3,8)(6,7)(11,21)(15,20)(22,36)(23,37)(28,33)(29,34)(30,35)(38,40)2915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26893);