Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C673 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #14582089 |
| commutator, hypocenter | C673 | C16 |
| Fitting | C4×C673 | C4 |
| socle, prime radical | C2×C673 | C8 |
| cosocle | #19129087 | C2 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|a^2=b,b^2=c,c^2=d,e^a=e^58,e^b=e^672688 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#24924646, #36340550, #36340551, … |
| maximal normal subgroup of | C2×#24924646, #36340550, #36340551, … |
| maximal quotient of | #36340527, C2×#24924646 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 43);