Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C42 |
No aliases for this group.
| Fitting | C4×#95×C79 ⋊ C2 |
| Sylow | C79 ⋊ #15142 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D79 |
| commutator, socle, cosocle | C24×C79 | C24 |
| Fitting | C4×#95×C79 | C2 |
| hypercenter | C4×#95 | D79 |
| hypocenter | C79 | #15142 |
| LCS | G ▷ C24×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
4382 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 4382 conjugacy classes of subgroups — too many to draw. Only its 515 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|b^2=e,c^2=f,d^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^78,c^b=cg3184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 106275);