Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#33539 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C79 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ C2×#131×C79 ◁ G | |
1130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2)(3,14)(4,18)(5,13)(6,12)(7,10)(8,15)(9,16)(11,21)(17,29)(19,30)(20,24)(22,28)(23,27)(25,31)(26,32)(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);(1,3)(2,8)(4,19)(5,16)(6,23)(7,17)(9,24)(10,25)(11,27)(12,26)(13,30)(14,18)(15,21)(20,31)(22,32)(28,29);(1,3)(2,9)(4,15)(5,23)(6,16)(7,17)(8,24)(10,27)(11,25)(12,29)(13,14)(18,30)(19,21)(20,32)(22,31)(26,28);(2,10)(8,25)(9,27)(11,24)(12,13)(14,29)(18,28)(26,30)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 26527);