Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×Q8×D53 |
| Fitting | C23×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D53 |
| commutator | C2×C53 | C26 |
| Frattini | C2 | C25×D53 |
| Fitting | C23×Q8×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C23×Q8 | D53 |
| hypocenter | C53 | C24×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
6264 conjugacy classes of subgroups.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1446, #27306476, #27306479, … |
| maximal normal subgroup of | D53×#1446, #27306476, #27306479, … |
| maximal quotient of | C23×C4⋊C4×D53, C22×C4×Q8×D53, C23×#13133182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19304);