Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C53×C64 ⋊ C2 |
| Sylow | C53 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×D53 |
| commutator, socle | C2×C53 | C2×C32 |
| Fitting | C53×C64 | C2 |
| hypercenter | C64 | D53 |
| hypocenter | C53 | M128 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C32 ◁ C64 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^521744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×M128, C2×#20272925, #27305130, … |
| maximal normal subgroup of | D53×M128, C2×#20272925, #27305130, … |
| maximal quotient of | #27271896, #27271900, #27271987, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2720);