Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#19129096 |
| Fitting, socle | C2×C673 ⋊ C8 |
| derived, Sylow | C673 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19129096 |
| commutator, hypocenter | C673 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C673 | C8 |
| prime radical | C2×D673 | C4 |
| cosocle | #14582089 | C22 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C2 | |
22 conjugacy classes of subgroups.
184 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19129096, C22⋊#19129096, C4⋊#19129096, … |
| maximal normal subgroup of | C4×#19129096, C22⋊#19129096, C4⋊#19129096, … |
| maximal quotient of | C4×#19129096, C22⋊#19129096, C4⋊#19129096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 53);