Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | M64×D53 |
| Fitting | C53×M64 ⋊ C2 |
| Sylow | C53 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D53 |
| commutator, socle | C2×C53 | C22×C16 |
| Fitting | C53×M64 | C2 |
| hypercenter | M64 | D53 |
| hypocenter | C53 | C2×M64 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C16 ◁ M64 | |
112 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1398, #27304278, D53×#1400, … |
| maximal normal subgroup of | D53×#1398, #27304278, D53×#1400, … |
| maximal quotient of | D53×#1397, M64×Dic53, #27304268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6800);