Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24 |
| direct product | C79×#33690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C79 |
| prime radical | C79×#2190 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C2×C4×C79 ◁ C4×M16×C79 ◁ G | |
526 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)(4,15)(5,19)(6,11)(8,17)(9,13)(10,14)(12,27)(16,31)(18,30)(20,28)(21,25)(22,24)(23,29)(26,32)(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);(1,3,6,14)(2,7,11,10)(4,12,16,18)(5,20,22,13)(8,23,26,25)(9,19,28,24)(15,30,31,27)(17,21,32,29);(1,4)(2,8)(3,12)(5,21)(6,16)(7,23)(9,27)(10,25)(11,26)(13,17)(14,18)(15,19)(20,32)(22,29)(24,31)(28,30);(4,12,16,18)(5,22)(8,25,26,23)(9,28)(13,20)(15,27,31,30)(17,21,32,29)(19,24)2686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 26678);