Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#13133151 |
| Sylow | C53 ⋊ C22×#107 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D212 |
| commutator | C4×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C23×C8×C53 | C2 |
| socle | C24×C53 | D4 |
| hypercenter | C23×C8 | D53 |
| hypocenter | C53 | C22×#107 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
600 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289990, #27289992, #27289994, … |
| maximal normal subgroup of | #27289990, #27289992, #27289994, … |
| maximal quotient of | C22×#16810376, C2×#20273474, C2×#20273490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13085);