Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8 |
No aliases for this group.
| Sylow | C7 ⋊ #17334 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C23×D7 |
| commutator, socle | C22×C7 | C22×C42 |
| Fitting | C7×#2920 | C2 |
| prime radical | C24×C7 | C42 |
| cosocle | C42×C7 | C24 |
| hypercenter | #2920 | D7 |
| hypocenter | C7 | #17334 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C42 ◁ #2920 | |
806 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,e^2=g,f^2=h,c^a=cg,i^a=i^6,c^b=ch,d^b=dg256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 135285);