Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#23995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C79 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| socle | C2×C79 | #2404 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C79 ◁ C22×C4×C79 ◁ G | |
1164 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)(3,7)(4,8)(5,10)(6,11)(9,13)(12,23)(14,21)(15,32)(16,24)(17,25)(18,27)(19,28)(20,29)(22,31)(26,30)(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)(2,7)(4,15,16,31)(5,14)(6,13)(8,22,24,32)(9,11)(10,21)(12,17,29,18)(19,30)(20,25,23,27)(26,28);(1,4)(2,8)(3,12)(5,18)(6,16)(7,20)(9,23)(10,27)(11,24)(13,29)(14,31)(15,30)(17,19)(21,32)(22,26)(25,28);(1,3)(2,9)(4,12)(5,14)(6,13)(7,11)(8,23)(10,26)(15,17)(16,29)(18,31)(19,30)(20,24)(21,28)(22,27)(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, 16983);