Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#23603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C24×C79 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C23×C4×C79 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 115 points:
(5,6,11,14,10,15,9,23)(7,16,25,27,18,33,19,12)(8,13,24,29,22,30,21,31)(17,32,35,26,34,28,20,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,2)(3,4)(5,7,9,19,10,18,11,25)(6,12,14,16,15,27,23,33)(8,20,21,34,22,35,24,17)(13,28,29,36,30,32,31,26);(2,4)(5,8,10,22)(6,13,15,30)(7,17,18,34)(9,24,11,21)(12,26,27,36)(14,31,23,29)(16,32,33,28)(19,35,25,20);(7,18)(12,27)(16,33)(17,34)(19,25)(20,35)(26,36)(28,32)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 16591);