Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C79 · Schur multiplier (H2) = C23 |
| direct product | C79×#13452 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C79 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C79 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C2×C42×C79 ◁ C2×C4×C8×C79 ◁ G | |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 107 points:
(5,6,9,11)(7,12,8,10)(13,14,16,20)(15,22,23,18)(17,19,25,27)(21,28,26,24)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,2)(3,4)(5,7,9,8)(6,10,11,12)(13,15,16,23)(14,18,20,22)(17,24,25,28)(19,26,27,21);(2,4)(5,8,9,7)(6,10,11,12)(14,19)(15,23)(17,24)(18,21)(20,27)(22,26)(25,28)4108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 6440);