Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C32×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×#6157 |
| commutator, socle | C2×C53 | C4×C16 |
| Fitting | C32×C53 | C4 |
| hypercenter | C32 | #6157 |
| hypocenter | C53 | #1397 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C16 ◁ C32 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^30,h^d=h^52496 conjugacy classes — view the full character table.
| maximal subgroup of | #28299314, #28299315, C2×#20289821, … |
| maximal normal subgroup of | #28299314, #28299315, C2×#20289821, … |
| maximal quotient of | #28298856, #88324⋊C32, (C2×#6157)⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19616);