Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D673 |
| Fitting | Q8×C673 ⋊ C2 |
| Sylow | C673 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D673 |
| commutator, socle, cosocle | C2×C673 | C23 |
| Fitting | Q8×C673 | C2 |
| prime radical | C2×D673 | C22 |
| hypercenter | Q8 | D673 |
| hypocenter | C673 | C2×Q8 |
| LCS | G ▷ C2×C673 ▷ C673 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
38 conjugacy classes of subgroups.
1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D673, Q16×D673, #36340506, … |
| maximal normal subgroup of | SD16×D673, Q16×D673, #36340506, … |
| maximal quotient of | C4⋊C4×D673, #36340442, Q8×Dic673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 37);