Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#24808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C79×#3068 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,7,11,8,12,6,4)(3,13,17,14,18,19,16,9)(5,21,23,26,24,20,22,10)(15,28,30,32,31,25,29,27)(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);(1,3,6,16,8,18,7,17)(2,9,11,13,12,14,4,19)(5,15,22,29,24,31,23,30)(10,25,21,27,26,28,20,32);(1,4)(2,6)(3,14)(5,20)(7,12)(8,11)(9,18)(10,22)(13,17)(15,28)(16,19)(21,24)(23,26)(25,31)(27,30)(29,32);(1,5,6,22,8,24,7,23)(2,10,11,21,12,26,4,20)(3,15,16,29,18,31,17,30)(9,25,13,27,14,28,19,32)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17796);