Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D673 |
| Fitting | C8×C673 ⋊ C2 |
| derived, Sylow | C673 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D673 |
| commutator, hypocenter | C673 | C2×C8 |
| Frattini | C4 | C2×D673 |
| Fitting | C8×C673 | C2 |
| socle | C2×C673 | C2×C4 |
| prime radical | C2×D673 | C4 |
| cosocle | C4×C673 | C22 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D673, #36340416, C2×C8×D673, … |
| maximal normal subgroup of | C16×D673, #36340416, C2×C8×D673, … |
| maximal quotient of | C8×Dic673, #36340389, #36340406, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 21);