Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1312 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C2×#6157 |
| commutator | C2×C53 | C4×C16 |
| Fitting | C4×C8×C53 | C4 |
| socle | C22×C53 | C4×C8 |
| hypercenter | C4×C8 | #6157 |
| hypocenter | C53 | #1312 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
92 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^b=h^30,h^d=h^52496 conjugacy classes — view the full character table.
| maximal subgroup of | #28298088, #28298089, #28298091, … |
| maximal normal subgroup of | #28298088, #28298089, #28298091, … |
| maximal quotient of | #28298088, #28298089, #28298256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19423);