Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C7 ⋊ #34214 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator | C22×C7 | C24×C4 |
| Fitting | C4×C7×#117 | C2 |
| socle, cosocle | C23×C7 | C25 |
| prime radical | C24×C7 | C24 |
| hypercenter | C4×#117 | D7 |
| hypocenter | C7 | #34214 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C4×#117 | |
2310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=h,b^2=gh,c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,i^a=i^6,d^b=df328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 330019);