Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C89 · Schur multiplier (H2) = C28 |
| direct product | C89×#61854 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C89 |
| prime radical | #532×C89 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ #533×C89 ◁ G | |
1648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 11392 |
A minimal faithful permutation representation — 5 generators on 121 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,21,25)(19,26,28,31)(20,24,22,29)(23,30,32,27)(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);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,18)(19,23)(20,29)(21,25)(22,24)(26,27)(28,32)(30,31);(17,19,21,28)(18,23,25,32)(20,27,22,30)(24,31,29,26);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(17,20,21,22)(18,24,25,29)(19,27,28,30)(23,31,32,26);(2,8)(6,9)(7,16)(14,15)(18,25)(23,32)(24,29)(26,31)4361 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 54842);