Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C7×#3566 ⋊ C2 |
| Sylow | C7 ⋊ #62755 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D7 |
| commutator, socle, cosocle | C22×C7 | C26 |
| Fitting | C7×#3566 | C2 |
| hypercenter | #3566 | D7 |
| hypocenter | C7 | #62755 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #3566 | |
Only the 3213 normal subgroups are shown; non-normal subgroups are omitted.
Polycyclic presentation:
2^8,7|c^2=h,d^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,c^b=cg,d^b=dh,i^d=i^6,i^e=i^6,i^f=i^6190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1077346);