Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C79×#2308 ⋊ C2 |
| Sylow | C79 ⋊ #35019 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D79 |
| commutator, socle, cosocle | C23×C79 | C25 |
| Fitting | C79×#2308 | C2 |
| prime radical | C22×#14579133 | C2 |
| hypercenter | #2308 | D79 |
| hypocenter | C79 | #35019 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #2308 | |
2994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|b^2=fg,c^2=g,b^a=bf,c^a=cg,e^a=eh,c^b=ch,d^b=dh,i^c=i^781780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 342746);