Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C7×#2396 ⋊ C2 |
| Sylow | C7 ⋊ #34551 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C7×#2396 | C2 |
| prime radical | #89732 | C22 |
| hypercenter | #2396 | D7 |
| hypocenter | C7 | #34551 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C22×C4 ◁ #2396 | |
2082 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=h,d^2=g,e^2=f,b^a=bf,c^a=cg,c^b=ch,i^b=i^6,i^c=i^6,i^d=i^6,i^e=i^6220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 335883);