Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C4×C7×H(5,𝔽2) ⋊ C2 |
| Sylow | C7 ⋊ #62800 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C26 |
| Frattini | C22 | C25×D7 |
| Fitting | C4×C7×H(5,𝔽2) | C2 |
| hypercenter | C4×H(5,𝔽2) | D7 |
| hypocenter | C7 | #62800 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ C4×H(5,𝔽2) | |
7856 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|e^2=h,f^2=g,b^a=bg,c^a=ch,e^a=eh,i^b=i^6,d^c=dh292 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1077953);