Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C82×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1335 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D424 |
| commutator | C8×C53 | C2×C8 |
| Frattini | C4×C8 | C2×D53 |
| Fitting | C82×C53 | C2 |
| socle | C2×C53 | D4⋊C8 |
| hypercenter | C82 | D53 |
| hypocenter | C53 | #1335 |
| LCS | G ▷ C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^52,c^b=ce,e^b=eg,h^b=h^521708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1335, C2×#20272689, #27293877, … |
| maximal normal subgroup of | D53×#1335, C2×#20272689, #27293877, … |
| maximal quotient of | #27270742, #27270745, #27270760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2484);