Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C79 · Schur multiplier (H2) = C28 |
| direct product | C79×#34602 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C79 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C79 |
| socle | C23×C79 | C25 |
| prime radical | C2×#121×C79 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C79 ◁ G | |
2294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(3,4)(5,6)(7,10)(8,9)(11,12)(13,14)(15,18)(16,19)(17,20)(21,25)(22,26)(23,27)(24,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(6,9)(10,12)(13,15,17,22)(14,18,20,26)(16,23,24,21)(19,27,28,25);(2,4)(13,16,17,24)(14,19,20,28)(15,21,22,23)(18,25,26,27);(14,20)(18,26)(19,28)(25,27);(5,7,8,11)(6,10,9,12)5056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 27590);