Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C79 · Schur multiplier (H2) = C214 |
| direct product | C2×C79×#3449 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C79 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C79 |
| socle | C23×C79 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C79 ◁ G | |
11662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 6 generators on 101 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)(84,85)(86,87)(88,94)(89,93)(90,92)(91,95)(96,100)(97,99)(98,101);(86,88)(87,91)(89,96)(90,95)(92,94)(93,98)(97,101)(99,100);(83,85)(88,95)(91,94)(96,101)(98,100);(87,92)(91,94)(93,99)(98,100);(86,89,90,97)(87,93,92,99)(88,96,95,101)(91,98,94,100)6952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 55671);