Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator | C2×C53 | C22×C42 |
| Fitting | C4×M16×C53 | C2 |
| socle | C22×C53 | C23×C4 |
| hypercenter | C4×M16 | D53 |
| hypocenter | C53 | #2875 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,e^2=g,b^a=bg,h^a=h^52,d^c=dg,h^d=h^521108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27280902, #27280906, #27280909, … |
| maximal normal subgroup of | #27280902, #27280906, #27280909, … |
| maximal quotient of | #27349686, #27349707, #27349766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12939);