Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C79×#3444 ⋊ C2 |
| Sylow | C79 ⋊ #412 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C23×D79 |
| commutator, socle, cosocle | C22×C79 | C26 |
| Frattini | C22 | C25×D79 |
| Fitting | C79×#3444 | C2 |
| hypercenter | #3444 | D79 |
| hypocenter | C79 | #412 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C42 ◁ #3444 | |
7812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|e^2=h,f^2=g,b^a=bg,c^a=ch,d^c=dh,i^d=i^782284 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1076676);