Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C79 · Schur multiplier (H2) = C23 |
| direct product | C79×#12946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | #447 |
| commutator | C2×C8 | C22×C4×C79 |
| Frattini, cosocle | C22×C8 | C23×C79 |
| prime radical | C2×#135×C79 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ #405×C79 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 115 points:
(1,2,4,3)(5,6,10,15)(7,17,20,36)(8,12,23,29)(9,14,25,30)(11,26,22,16)(13,31,33,19)(18,35,24,34)(21,28,27,32)(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);(1,3,4,2)(6,12)(8,9)(11,22)(13,28)(14,16)(15,29)(17,35)(18,31)(19,24)(21,27)(23,25)(26,30)(32,33)(34,36);(5,7)(6,13)(8,19)(9,24)(10,20)(11,27)(12,28)(14,17)(15,33)(16,35)(18,25)(21,22)(23,31)(26,34)(29,32)(30,36)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 5934);