Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C7×#2561 ⋊ C2 |
| Sylow | C7 ⋊ #36703 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2561 | C2 |
| hypercenter | #2561 | D7 |
| hypocenter | C7 | #36703 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2561 | |
4062 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|b^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^6,c^b=ch,d^b=dfh,i^d=i^6166 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 376317);