Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C42×C7×Q8 ⋊ C2 |
| Sylow | C7 ⋊ #34552 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C22×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C42×C7×Q8 | C2 |
| prime radical | C23×D7 | C24 |
| hypercenter | C42×Q8 | D7 |
| hypocenter | C7 | #34552 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C42 ◁ C42×Q8 | |
1962 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|b^2=h,c^2=h,d^2=g,e^2=f,b^a=bf,c^a=cg,i^a=i^6,c^b=ch328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 335888);