Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C29 |
| direct product | C53×#61097 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C53×#532 ◁ G | |
2654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 89 points:
(1,2)(3,4)(6,11)(8,19)(9,22)(12,25)(13,29)(14,23)(15,28)(16,31)(17,24)(20,26)(27,30)(32,35)(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);(5,6,10,14)(7,15,18,25)(8,20,19,13)(9,23,22,11)(12,24,28,17)(16,32,31,30)(21,26,34,29)(27,33,35,36);(2,4)(8,19)(13,20)(16,31)(21,34)(26,29)(27,35)(30,32)(33,36);(5,7,10,18)(6,12,14,28)(8,16,19,31)(9,24,22,17)(11,25,23,15)(13,27,20,35)(21,36,34,33)(26,32,29,30);(5,8)(6,13)(7,16)(9,21)(10,19)(11,26)(12,27)(14,20)(15,30)(17,33)(18,31)(22,34)(23,29)(24,36)(25,32)(28,35)2915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54085);