Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43 |
No aliases for this group.
| Sylow | C79 ⋊ #13750 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D79 |
| commutator | C2×C79 | C2×C43 |
| Fitting | C2×#376×C79 | C2 |
| socle, prime radical, cosocle | C24×C79 | C24 |
| hypercenter | C2×#376 | D79 |
| hypocenter | C79 | #13750 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ C2×#376 | |
2078 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 2078 conjugacy classes of subgroups — too many to draw. Only its 987 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20224 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=h,d^2=e,b^a=be,d^a=de,i^a=i^78,c^b=ce3256 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90654);