Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#33633 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| prime radical | C2×#135×C53 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ #117×C53 ◁ C53×#405 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,15)(13,26)(14,19)(17,23)(18,24)(20,30)(21,27)(22,36)(25,29)(28,37)(31,35)(32,34)(33,38)(39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,4,8)(2,5,6,7)(11,20)(16,30)(21,33)(22,34)(27,38)(31,39)(32,36)(35,40);(10,15)(12,23)(13,24)(16,27)(17,18)(19,29)(21,35)(22,34)(25,37)(26,28)(30,38)(31,32)(33,40)(36,39);(9,11,14,20)(10,16,19,30)(12,21,25,33)(13,22,24,34)(15,27,29,38)(17,31,28,39)(18,32,26,36)(23,35,37,40)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26621);