Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#13329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C22×D8×C53 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ C2×C4×C8×C53 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,4)(9,10,15,21)(11,22,26,35)(12,27,13,17)(14,33,30,20)(16,24,37,23)(18,32,19,29)(25,39,34,38)(28,40,31,36)(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);(2,4)(5,6)(7,8)(9,11,15,26)(10,16,21,37)(12,28,13,31)(14,34,30,25)(17,35,27,22)(18,38,19,39)(20,40,33,36)(23,32,24,29);(6,8)(10,17)(12,29)(13,32)(14,30)(16,35)(18,33)(19,20)(21,27)(22,37)(23,28)(24,31)(25,34)(36,38)(39,40)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6317);