Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×#2327 ⋊ C2 |
| Sylow | C7 ⋊ C4×#541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator | C22×C7 | C24×C4 |
| Fitting | C7×#2327 | C2 |
| socle, cosocle | C23×C7 | C25 |
| prime radical | C23×D7 | C24 |
| hypercenter | #2327 | D7 |
| hypocenter | C7 | C4×#541 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2327 | |
2070 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=h,b^2=g,d^2=f,e^2=fh,b^a=bf,c^a=cg,d^a=df,i^a=i^6,c^b=cf,i^b=i^6,i^c=i^6,i^e=i^6220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 328718);