Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24986 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24 |
| direct product | C79×#24986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C79 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| socle | C2×C79 | #2420 |
| prime radical | C79×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C79 ◁ C22×C4×C79 ◁ G | |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2)(3,10)(4,17)(5,22)(6,12)(7,13)(8,15)(9,20)(11,23)(14,24)(16,25)(18,26)(19,28)(21,27)(29,32)(30,31)(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);(1,3,6,15,7,16,23,5)(2,8,11,10,13,22,12,25)(4,18,20,30,21,29,19,14)(9,26,17,24,28,32,27,31);(1,4)(2,9)(3,14)(5,18)(6,19)(7,21)(8,24)(10,26)(11,27)(12,17)(13,28)(15,29)(16,30)(20,23)(22,31)(25,32);(1,5,6,3,7,15,23,16)(2,10,11,22,13,25,12,8)(4,18,19,14,21,29,20,30)(9,26,27,31,28,32,17,24)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17974);