Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#405 ⋊ C2 |
| Sylow | C53 ⋊ #2969 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#405 | C2 |
| hypercenter | #405 | D53 |
| hypocenter | C53 | #2969 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #405 | |
370 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,c^b=cg,h^b=h^52,d^c=dg1090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#2969, C2×#20283715, #28248639, … |
| maximal normal subgroup of | D53×#2969, C2×#20283715, #28248639, … |
| maximal quotient of | #27382356, #27382364, #27382397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13510);