Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C79 ⋊ #36732 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D79 |
| commutator, socle, cosocle | C23×C79 | C25 |
| Fitting | C2×#381×C79 | C2 |
| prime radical | C25×C79 | C23 |
| hypercenter | C2×#381 | D79 |
| hypocenter | C79 | #36732 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×#381 | |
1770 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=fg,c^2=f,d^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^78,c^b=ch,d^b=dfh2236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 376793);