Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60750 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C79 · Schur multiplier (H2) = C27×C4 |
| direct product | C79×#60805 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C79 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C42×C79 ◁ G | |
2196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,17)(12,21)(13,14)(15,20)(16,22)(18,24)(19,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3,4,8)(2,5,6,7)(10,14)(11,18)(16,21)(19,20);(3,8)(5,7)(9,11)(10,15)(12,19)(13,18)(14,23)(16,24)(17,21)(20,22);(2,6)(5,7)(10,14)(15,23)(16,21)(17,24);(9,12,13,22)(10,16,14,21)(11,19,18,20)(15,24,23,17)4108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 53793);