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 | C2 | #19129096 |
| commutator, hypocenter | C673 | C16 |
| Fitting, socle, prime radical | C2×C673 | C8 |
| cosocle | #19129094 | C2 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|a^2=b,b^2=c,c^2=d,e^a=e^609,e^b=e^58,e^c=e^672184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#24924655, #36340572, #36340573, … |
| maximal normal subgroup of | C2×#24924655, #36340572, #36340573, … |
| maximal quotient of | #36340567, C2×#24924655 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 52);