Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C79 · Schur multiplier (H2) = C22 |
| direct product | C79×#10483 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C79 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C79 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C2×C42×C79 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 107 points:
(5,6,7,9)(8,10,12,11)(13,14)(15,23)(16,20)(17,27)(18,22)(19,25)(21,24)(26,28)(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);(1,2)(3,4)(6,9)(10,11)(13,15,18,16)(14,19,22,28)(17,26,24,25)(20,27,23,21);(2,4)(6,10)(8,12)(9,11)(13,16,17,26,18,15,24,25)(14,20,21,19,22,23,27,28)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 3471);