Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C2×C79×#2187 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C79 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C79 |
| prime radical | C23×D8×C79 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C23×C4×C79 ◁ C23×C8×C79 ◁ G | |
1382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(3,4)(5,6)(7,8,11,15)(9,12,18,21)(10,19,17,14)(13,22,20,16);(8,12)(9,16)(10,17)(13,14)(15,21)(18,22)(19,20);(4,6)4582 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 26499);