Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1818 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D53 |
| commutator, socle | C23×C53 | C22×C4 |
| Fitting | C2×#117×C53 | C2 |
| hypercenter | C2×#117 | D53 |
| hypocenter | C53 | #1818 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
292 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^52,c^b=cg1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271412, #27271416, #27276271, … |
| maximal normal subgroup of | #27271412, #27271416, #27276271, … |
| maximal quotient of | #27277427, #27277430, #27277433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4581);