Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#405 ⋊ C2 |
| Sylow | C53 ⋊ C4×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D53 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#405 | C2 |
| socle | C22×C53 | C23×C4 |
| hypercenter | #405 | D53 |
| hypocenter | C53 | C4×#131 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ #405 | |
572 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,e^2=g,h^b=h^52,d^c=dg,h^d=h^521120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299139, #27299144, #27300028, … |
| maximal normal subgroup of | #27299139, #27299144, #27300028, … |
| maximal quotient of | #27349679, C8×#13133225, #27349703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12932);