Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C42 | C2×D53 |
| commutator | C2×C53 | C82 |
| Fitting | C2×C4×C8×C53 | C2 |
| socle | C23×C53 | C42 |
| hypercenter | C2×C4×C8 | D53 |
| hypocenter | C53 | #1273 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^b=h^521744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270864, #27270865, #27270877, … |
| maximal normal subgroup of | #27270864, #27270865, #27270877, … |
| maximal quotient of | #27270618, #27270619, #27270620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2337);