Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C7×#3515 ⋊ C2 |
| Sylow | C7 ⋊ #62805 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D7 |
| commutator, socle, cosocle | C22×C7 | C26 |
| Fitting | C7×#3515 | C2 |
| hypercenter | #3515 | D7 |
| hypocenter | C7 | #62805 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #3515 | |
7104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=h,e^2=h,f^2=g,b^a=bg,c^a=ch,e^a=eh,i^b=i^6,d^c=dh,i^e=i^6,i^f=i^6220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1078024);