Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C23×C4 |
| direct product | C79×#33785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C79 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ C2×C4×C8×C79 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 119 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,19)(12,24)(13,15)(14,28)(16,22)(17,25)(18,26)(20,34)(21,35)(23,36)(27,39)(29,32)(30,38)(31,40)(33,37)(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);(1,3,4,8)(2,5,6,7)(10,15)(16,30)(17,24)(18,31)(19,35)(28,39)(32,33)(34,36);(3,8)(5,7)(9,11)(10,16)(12,20)(13,21)(14,29)(15,30)(17,32)(18,34)(19,28)(22,26)(23,25)(24,33)(27,37)(31,36)(35,39)(38,40);(2,6)(5,7)(9,12,13,25)(10,17,15,24)(11,20,21,23)(14,26,27,40)(16,32,30,33)(18,28,31,39)(19,36,35,34)(22,37,38,29)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 26773);