Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C79 · Schur multiplier (H2) = C24 |
| direct product | C79×#13068 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #1893 |
| commutator | C2×C8 | C22×C4×C79 |
| Frattini, cosocle | C22×C8 | C23×C79 |
| prime radical | C2×#472×C79 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ C2×#131×C79 ◁ G | |
470 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)(3,13,16,26)(4,17)(5,11)(6,21)(7,12)(8,10)(9,15,25,22)(14,24,18,27)(19,28)(20,31)(23,32,30,29)(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);(1,2,8,17,6,11,20,28,7,12,19,31,5,21,4,10)(3,9,23,29,15,26,14,24,16,25,30,32,22,13,18,27);(1,3)(2,9)(4,18)(5,22)(6,15)(7,16)(8,23)(10,27)(11,26)(12,25)(13,21)(14,20)(17,29)(19,30)(24,28)(31,32)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 6056);