Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C79 · Schur multiplier (H2) = C22 |
| direct product | C79×#13469 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2065 |
| commutator, Frattini, cosocle | C22×C8 | C23×C79 |
| prime radical | C2×#135×C79 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ #405×C79 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,2,9,14,8,15,7,27)(3,11,18,32,19,28,25,31)(4,20,17,30,21,29,24,10)(5,22,26,13,6,23,16,12)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(1,3,5,17,7,18,16,21,8,19,6,24,9,25,26,4)(2,10,12,11,14,29,22,31,15,30,13,28,27,20,23,32);(1,4)(2,11)(3,16)(5,18)(6,25)(7,24)(8,21)(9,17)(10,13)(12,30)(14,32)(15,28)(19,26)(20,23)(22,29)(27,31)2686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 6457);