Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×#2965 ⋊ C2 |
| Sylow | C7 ⋊ #60344 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C24×D7 |
| commutator, socle | C22×C7 | C24×C4 |
| Fitting | C7×#2965 | C2 |
| prime radical | #90524 | C4 |
| cosocle | C2×C4×C7 | C25 |
| hypercenter | #2965 | D7 |
| hypocenter | C7 | #60344 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #2965 | |
1664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=f,c^2=f,e^2=g,g^2=h,b^a=bf,c^a=ch,d^a=df,i^a=i^6,c^b=cf,d^b=dh,e^b=eh,i^b=i^6244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1035825);