Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#25437 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C2×AGL(1,ℤ/8)×C79 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,4,3)(5,6,12,17)(7,18,21,30)(8,14,20,13)(9,23,27,36)(10,28,11,16)(15,26,32,25)(19,31,34,29)(22,35,24,33)(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);(1,2,4,3)(5,7,10,20,12,21,11,8)(6,13,16,18,17,14,28,30)(9,19,25,24,27,34,26,22)(15,29,23,33,32,31,36,35);(1,3)(2,4)(5,8)(6,14)(7,10)(9,24)(11,21)(12,20)(13,17)(15,29)(16,30)(18,28)(19,26)(22,27)(23,33)(25,34)(31,32)(35,36);(5,9,10,25,12,27,11,26)(6,15,16,23,17,32,28,36)(7,19,20,24,21,34,8,22)(13,29,18,33,14,31,30,35)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 18425);