Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | Aut(G) order 14472192 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5384 |
| Fitting | C8×C673 ⋊ C2 |
| Sylow | C673 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D2692 |
| commutator, cosocle | C4×C673 | C22 |
| Frattini | C4 | C2×D673 |
| Fitting | C8×C673 | C2 |
| socle | C2×C673 | D4 |
| hypercenter | C8 | D673 |
| hypocenter | C673 | D8 |
| LCS | G ▷ C4×C673 ▷ C2×C673 ▷ C673 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|c^2=d,b^a=bc,c^a=cd,e^a=e^672,c^b=cd,e^b=e^6722695 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36340418, D10768, #36340420, … |
| maximal normal subgroup of | #36340418, D10768, #36340420, … |
| maximal quotient of | #36340399, #36340411, D10768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 26);