Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C89 · Schur multiplier (H2) = C23×C4 |
| direct product | C89×#21281 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C89 | C22×D4 |
| commutator | C2×C4 | C23×C4×C89 |
| Frattini, cosocle | C22×C4 | C24×C89 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ #376×C89 ◁ G | |
766 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 22784 |
A minimal faithful permutation representation — 4 generators on 117 points:
(1,2,4,3)(5,6)(7,10)(8,9)(11,12)(15,21)(16,22)(18,24)(20,25)(23,27)(26,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117);(1,3,4,2)(6,9)(10,12)(13,14)(15,18)(16,20)(17,19)(21,24)(22,25)(23,26)(27,28);(13,15,22,27,17,23,16,21)(14,18,25,28,19,26,20,24);(5,7,8,11)(6,10,9,12)(14,19)(18,26)(20,25)(24,28)5696 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 14269);