Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#88322 |
| derived, Sylow | C53 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D53 |
| commutator, hypocenter | C53 | C24×C8 |
| Frattini | C4 | C24×D53 |
| Fitting | C24×C4×C53 | C2 |
| socle | C25×C53 | C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C24×C4 | |
1976 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289315, #27289317, #27289341, … |
| maximal normal subgroup of | #27289315, #27289317, #27289341, … |
| maximal quotient of | C23×C4×#88322, C23×C22⋊#88322, C23×C4⋊#88322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19209);