Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C26 |
| direct product | C53×#22465 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator | C2×C4 | C23×C4×C53 |
| Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C2×C53×#578 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
1312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,3,4)(5,6,10,14,11,16,9,15)(7,17,19,12,21,27,20,28)(8,13,23,31,25,32,24,30)(18,33,34,26,35,29,22,36)(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);(5,7)(6,12)(8,22)(9,20)(10,19)(11,21)(13,29)(14,27)(15,17)(16,28)(18,23)(24,35)(25,34)(26,30)(31,36)(32,33);(5,6,11,16)(7,12,21,28)(8,13,25,32)(9,14,10,15)(17,20,27,19)(18,26,35,36)(22,29,34,33)(23,30,24,31);(5,8)(6,13)(7,18)(9,24)(10,23)(11,25)(12,26)(14,31)(15,30)(16,32)(17,33)(19,34)(20,22)(21,35)(27,29)(28,36)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 15453);