Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#13319 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
572 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(5,6)(7,16)(8,11)(9,25)(10,15)(12,18)(13,21)(14,23)(17,29)(19,31)(20,30)(22,32)(24,28)(26,33)(27,35)(34,36)(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)(6,11)(8,21)(9,23)(12,26)(13,14)(15,28)(16,29)(17,33)(18,19)(22,34)(24,35)(25,27)(30,32)(31,36);(2,4)(5,7)(6,12)(8,22)(9,19)(10,20)(11,26)(13,32)(14,30)(15,31)(16,25)(17,24)(18,23)(21,34)(27,29)(28,36)(33,35)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6307);