Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C89 · Schur multiplier (H2) = C214 |
| direct product | C89×#63091 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | C24×D4 |
| commutator, Frattini, cosocle | C4 | C26×C89 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ #585×C89 ◁ G | |
10894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 2848 |
A minimal faithful permutation representation — 6 generators on 121 points:
(1,2)(3,8)(4,9)(5,7)(6,11)(10,17)(12,20)(13,21)(14,18)(15,23)(16,19)(22,27)(24,28)(25,30)(26,29)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(2,7)(5,17)(8,18)(9,19)(10,11)(14,27)(16,28)(20,29)(21,22)(23,24)(26,32)(30,31);(1,3)(2,8)(4,12)(5,14)(6,13)(7,18)(9,20)(10,22)(11,21)(15,25)(16,26)(17,27)(19,29)(23,30)(24,31)(28,32);(1,4)(2,9)(3,12)(5,16)(6,15)(7,19)(8,20)(10,24)(11,23)(13,25)(14,26)(17,28)(18,29)(21,30)(22,31)(27,32);(4,15)(9,23)(12,25)(16,28)(19,24)(20,30)(26,32)(29,31);(3,13)(8,21)(12,25)(14,27)(18,22)(20,30)(26,32)(29,31)7298 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56079);