Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C26 |
| direct product | C53×#22468 |
| 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 | |
1316 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)(7,17,19,12,21,28,20,29)(8,22,24,31,26,13,25,32)(18,30,34,36,35,33,23,27)(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)(8,23)(9,20)(10,19)(11,21)(13,30)(14,28)(15,17)(16,29)(18,24)(22,33)(25,35)(26,34)(27,31)(32,36);(5,6,11,16)(7,12,21,29)(8,13,26,22)(9,14,10,15)(17,20,28,19)(18,27,35,36)(23,30,34,33)(24,31,25,32);(5,8)(6,13)(7,18)(9,25)(10,24)(11,26)(12,27)(14,32)(15,31)(16,22)(17,33)(19,34)(20,23)(21,35)(28,30)(29,36)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 15456);