Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #17328 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C23×D7 |
| commutator, socle | C22×C7 | C22×C42 |
| Fitting | C7×#2922 | C2 |
| prime radical | C2×C7×#41 | C2×C4 |
| cosocle | C42×C7 | C24 |
| hypercenter | #2922 | D7 |
| hypocenter | C7 | #17328 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C42 ◁ #2922 | |
750 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=e,b^2=f,e^2=g,f^2=h,c^a=ch,i^b=i^6,d^c=dg280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 135230);