Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#16811040 |
| Sylow | C53 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D53 |
| commutator | C2×C53 | C23×C8 |
| Frattini | C8 | C23×D53 |
| Fitting | C2×#131×C53 | C2 |
| socle | C22×C53 | C22×C8 |
| hypercenter | C2×#131 | D53 |
| hypocenter | C53 | C2×#504 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C2×#131 | |
368 conjugacy classes of subgroups.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299190, #27299191, #27299196, … |
| maximal normal subgroup of | #27299190, #27299191, #27299196, … |
| maximal quotient of | C2×#20276312, C4×#16811040, C2×#20276329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17609);