Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#431 ⋊ C2 |
| Sylow | C53 ⋊ #2993 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#431 | C2 |
| hypercenter | #431 | D53 |
| hypocenter | C53 | #2993 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #431 | |
354 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^52,c^b=ce,d^b=dg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27354152, #27354156, #27354167, … |
| maximal normal subgroup of | #27354152, #27354156, #27354167, … |
| maximal quotient of | #27382916, #27382956, #27383052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13661);