Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#33584 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C79 |
| prime radical | C2×#509×C79 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ C2×C4×C8×C79 ◁ G | |
722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 115 points:
(2,4)(5,6)(7,15)(8,20)(9,11)(10,24)(12,18)(13,21)(14,22)(16,30)(17,31)(19,32)(23,35)(25,28)(26,34)(27,36)(29,33)(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);(1,2,3,4)(6,11)(12,26)(13,20)(14,27)(15,31)(24,35)(28,29)(30,32);(5,7)(6,12)(8,16)(9,17)(10,25)(11,26)(13,28)(14,30)(15,24)(18,22)(19,21)(20,29)(23,33)(27,32)(31,35)(34,36);(5,8,9,21)(6,13,11,20)(7,16,17,19)(10,22,23,36)(12,28,26,29)(14,24,27,35)(15,32,31,30)(18,33,34,25)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 26572);