Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×C8×D53 |
| Fitting | C23×C8×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D53 |
| commutator, hypocenter | C53 | C24×C8 |
| Frattini | C4 | C24×D53 |
| Fitting | C23×C8×C53 | C2 |
| socle | C24×C53 | C2×C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289314, #27289340, #27289346, … |
| maximal normal subgroup of | #27289314, #27289340, #27289346, … |
| maximal quotient of | C22×C4×C8×D53, C23×C8×Dic53, C22×C22⋊C8×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19208);