Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C7 ⋊ #34530 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator | C22×C7 | C24×C4 |
| Fitting | C2×C7×#564 | C2 |
| socle, prime radical, cosocle | C23×C7 | C25 |
| hypercenter | C2×#564 | D7 |
| hypocenter | C7 | #34530 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×#564 | |
1800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1792 |
Polycyclic presentation:
2^8,7|a^2=h,b^2=g,c^2=fh,d^2=g,e^2=h,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^6,c^b=cg,d^b=df,i^c=i^6,i^e=i^6190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 335741);