Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#13385 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C53×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 points:
(2,3)(5,6)(7,17)(8,13)(9,12)(10,15)(11,19)(14,24)(16,23)(18,26)(20,34)(21,30)(22,28)(25,35)(27,33)(29,36)(31,32)(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);(1,2)(3,4)(5,7)(6,11)(8,19)(9,20)(10,18)(12,27)(13,17)(14,25)(15,30)(16,26)(21,23)(22,33)(24,32)(28,34)(29,31)(35,36);(1,3,4,2)(6,12)(7,18)(9,24)(10,23)(11,25)(13,28)(14,16)(15,29)(17,31)(19,21)(20,33)(22,36)(26,34)(27,30)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6373);