Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#24472 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ G | |
1372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 1264 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2,6,9,7,10,5,4)(3,11,12,8,14,15,13,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,3)(2,8)(4,11)(5,13)(6,12)(7,14)(9,15)(10,16);(1,4)(2,5)(3,8)(6,10)(7,9)(11,12)(13,15)(14,16);(1,4)(2,6)(3,11)(5,10)(7,9)(8,12)(13,16)(14,15)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17460);