Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C2×C79×#2032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | #393 |
| commutator, Frattini, cosocle | C24 | C24×C79 |
| prime radical | C23×D4×C79 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C25×C79 ◁ G | |
1434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 97 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79)(80,81);(82,83)(84,87)(85,92,94,88)(86,89)(90,97,93,95)(91,96);(82,84)(83,87)(85,93,94,90)(86,91)(88,95,92,97)(89,96);(82,85)(83,88)(84,90)(86,94)(87,95)(89,92)(91,93)(96,97)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 16461);