Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#131×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C23×D53 |
| commutator, socle | C2×C53 | C24×C4 |
| Frattini | C4 | C24×D53 |
| Fitting | C2×#131×C53 | C2 |
| hypercenter | C2×#131 | D53 |
| hypocenter | C53 | #3573 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C8 ◁ C2×#131 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,f^2=g,e^b=eg,d^c=dg,h^e=h^521108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299539, #27299541, #27299542, … |
| maximal normal subgroup of | #27299539, #27299541, #27299542, … |
| maximal quotient of | #28247510, #28247511, #28247512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19221);