Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C673 ⋊ C2 |
| Sylow | C673 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D673 |
| commutator, socle | C2×C673 | C2×C4 |
| Fitting | C8×C673 | C2 |
| prime radical | C2×D673 | C4 |
| cosocle | C4×C673 | C22 |
| hypercenter | C8 | D673 |
| hypocenter | C673 | M16 |
| LCS | G ▷ C2×C673 ▷ C673 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|a^2=c,c^2=d,b^a=bd,e^b=e^6722698 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×D673, C2×#24924626, #36340483, … |
| maximal normal subgroup of | M16×D673, C2×#24924626, #36340483, … |
| maximal quotient of | #36340387, #36340389, #36340406, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 23);