Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25798 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25×C4 |
| direct product | C79×#25798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2433 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ G | |
1430 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)(3,11)(4,15)(5,18)(6,10)(7,13)(8,16)(9,19)(12,26)(14,25)(17,29)(20,28)(21,23)(22,30)(24,27)(31,32)(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);(1,3,5,13,6,14,19,23)(2,7,9,11,10,21,18,25)(4,12,16,27,17,28,30,31)(8,20,15,24,22,26,29,32);(1,2)(3,7,14,21)(4,8)(5,9)(6,10)(11,23,25,13)(12,20,28,26)(15,16)(17,22)(18,19)(24,31,32,27)(29,30);(1,4,5,16,6,17,19,30)(2,8,9,15,10,22,18,29)(3,12,13,27,14,28,23,31)(7,20,11,24,21,26,25,32)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 18786);