Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #2285 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C23 | C23×D53 |
| Fitting | C22×C42×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C22×C42 | D53 |
| hypocenter | C53 | #2285 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 | |
656 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^521720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27273631, #27273632, #27273643, … |
| maximal normal subgroup of | #27273631, #27273632, #27273643, … |
| maximal quotient of | #27305203, #27305208, C4×#16810483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6917);