Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C79 · Schur multiplier (H2) = C28 |
| direct product | C79×#62162 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C79 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ #529×C79 ◁ G | |
1702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 5 generators on 111 points:
(1,2,5,8)(3,9,10,6)(4,12,13,7)(11,14,16,15)(17,18,22,26)(19,27,30,23)(20,25,21,31)(24,28,32,29)(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);(1,3)(2,6)(4,11)(5,10)(7,14)(8,9)(12,15)(13,16)(17,19,22,30)(18,23,26,27)(20,28,21,29)(24,31,32,25);(17,20,22,21)(18,24,26,32)(19,28,30,29)(23,31,27,25);(3,10)(6,9)(11,16)(14,15)(17,20,22,21)(18,25,26,31)(19,29,30,28)(23,32,27,24);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(17,21,22,20)(18,25,26,31)(19,28,30,29)(23,32,27,24)3871 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 55150);