Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic673 |
| derived, Sylow | C673 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D673 |
| commutator, hypocenter | C673 | C42 |
| Frattini | C22 | C2×D673 |
| Fitting | C2×C4×C673 | C2 |
| socle, prime radical, cosocle | C22×C673 | C22 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic673, #36340387, #36340403, … |
| maximal normal subgroup of | C8×Dic673, #36340387, #36340403, … |
| maximal quotient of | #36340384, C8×Dic673, C4×#19129087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 16);