Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#11719924 |
| Fitting | C23×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C23×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22⋊D53 |
| commutator | C4×C53 | C25 |
| Frattini | C4 | C24×D53 |
| Fitting | C23×Q8×C53 | C2 |
| socle | C24×C53 | D4 |
| hypercenter | C23×Q8 | D53 |
| hypocenter | C53 | C23×SD16 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×Q8 | |
1720 conjugacy classes of subgroups.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27290893, #27290897, #27290920, … |
| maximal normal subgroup of | #27290893, #27290897, #27290920, … |
| maximal quotient of | C23×#13133137, C23×#13133141, C23×#13133148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19228);