Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#24462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C2×#578×C79 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ G | |
1302 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,3,4)(5,6,11,15)(7,17,13,28)(8,20,24,12)(9,26,27,19)(10,16,29,14)(18,34,31,30)(21,22,35,36)(23,32,25,33)(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);(5,7,11,13)(6,9,15,27)(8,21,24,35)(10,26,29,19)(12,30,20,34)(14,28,16,17)(18,23,31,25)(22,33,36,32);(2,4)(5,8,11,24)(6,12,15,20)(7,18,13,31)(9,22,27,36)(10,23,29,25)(14,32,16,33)(17,30,28,34)(19,35,26,21);(5,9)(6,13)(7,15)(8,22)(10,28)(11,27)(12,31)(14,19)(16,26)(17,29)(18,20)(21,33)(23,34)(24,36)(25,30)(32,35)3397 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17450);