Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#33610 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×#41×C53 ◁ C2×#131×C53 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(3,4)(6,11)(8,12)(9,19)(13,21)(14,29)(15,24)(17,25)(18,31)(20,26)(22,23)(27,32)(28,36)(30,35)(33,34)(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);(5,6,12,23,9,14,20,24,10,15,26,29,19,22,8,11)(7,13,25,34,18,28,30,32,16,27,35,36,31,33,17,21);(2,4)(7,16)(13,27)(17,30)(18,31)(21,32)(25,35)(28,33)(34,36);(5,7,10,16)(6,13,15,27)(8,17,20,30)(9,18,19,31)(11,21,24,32)(12,25,26,35)(14,28,22,33)(23,34,29,36)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26598);