Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C89 · Schur multiplier (H2) = C26 |
| direct product | C89×#32950 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| prime radical | C89×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C22×C4×C89 ◁ G | |
1282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 2848 |
A minimal faithful permutation representation — 4 generators on 121 points:
(2,7)(3,11)(5,18)(9,20)(10,21)(12,28)(13,14)(15,16)(19,23)(22,31)(25,26)(27,29)(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);(1,2,5,7,6,10,18,21)(3,8,13,19,14,24,11,23)(4,9,15,20,17,26,16,25)(12,22,28,30,29,31,27,32);(1,3)(2,8)(4,12)(5,13)(6,14)(7,19)(9,22)(10,24)(11,18)(15,28)(16,27)(17,29)(20,30)(21,23)(25,32)(26,31);(1,4)(2,9)(3,12)(5,15)(6,17)(7,20)(8,22)(10,26)(11,27)(13,28)(14,29)(16,18)(19,30)(21,25)(23,32)(24,31)4094 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 25938);