Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#33435 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C79 | C24 |
| commutator | C22 | C23×C8×C79 |
| Frattini, cosocle | C2×C8 | C24×C79 |
| socle | C22×C79 | C23×C8 |
| prime radical | #532×C79 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C79 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2)(3,4)(5,6,9,14,10,7,16,18,11,15,24,30,25,19,12,26)(8,20,22,34,23,32,31,36,21,13,28,29,35,17,27,33)(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);(2,4)(8,21)(13,20)(17,32)(22,28)(23,35)(27,31)(29,34)(33,36);(5,7,9,18,10,15,16,30,11,19,24,26,25,6,12,14)(8,17,22,33,23,20,31,34,21,32,28,36,35,13,27,29);(5,8)(6,13)(7,17)(9,22)(10,23)(11,21)(12,27)(14,29)(15,20)(16,31)(18,33)(19,32)(24,28)(25,35)(26,36)(30,34)6952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 26423);