Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C7×#3025 ⋊ C2 |
| Sylow | C7 ⋊ #60399 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D7×#120 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C7×#3025 | C2 |
| socle | C2×C7 | C22×#120 |
| hypercenter | #3025 | D7 |
| hypocenter | C7 | #60399 |
| LCS | G ▷ C23×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #3025 | |
5128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^8,7|b^a=bf,c^a=cg,g^b=gh,f^c=fh,e^d=eh,i^d=i^6,i^e=i^6154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1036317);