Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×M16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2873 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#6157 |
| commutator, socle | C2×C53 | C22×C42 |
| Fitting | C2×M16×C53 | C4 |
| hypercenter | C2×M16 | #6157 |
| hypocenter | C53 | #2873 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
564 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,e^2=g,d^a=dg,c^b=cg,h^b=h^30,h^f=h^52328 conjugacy classes — view the full character table.
| maximal subgroup of | #28306731, #28306733, #28306734, … |
| maximal normal subgroup of | #28306731, #28306733, #28306734, … |
| maximal quotient of | #28313755, #28313756, #28313757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21073);