Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#19129087 |
| derived, Sylow | C673 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D673 |
| commutator, hypocenter | C673 | C2×C8 |
| Frattini | C4 | C2×D673 |
| Fitting | C2×C4×C673 | C2 |
| socle, prime radical | C22×C673 | C4 |
| cosocle | C4×C673 | C22 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic673, C4×#19129087, #36340387, … |
| maximal normal subgroup of | C8×Dic673, C4×#19129087, #36340387, … |
| maximal quotient of | C4×#19129087, C22⋊#19129087, C4⋊#19129087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 22);