Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Sylow | C79 ⋊ C4×#382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D79 |
| commutator | C22×C79 | C22×C42 |
| Fitting | C79×#1434 | C2 |
| socle, prime radical, cosocle | C24×C79 | C24 |
| hypercenter | #1434 | D79 |
| hypocenter | C79 | C4×#382 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ #1434 | |
1742 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20224 |
Polycyclic presentation:
2^8,79|a^2=g,b^2=h,c^2=ef,d^2=eh,b^a=be,c^a=cf,i^d=i^782296 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90795);