Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C673 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14582089 |
| commutator, socle | C2×C673 | C2×C4 |
| Fitting, prime radical | C22×C673 | C4 |
| cosocle | Dic673 | C22 |
| hypercenter | C22 | #14582089 |
| hypocenter | C673 | M16 |
| LCS | G ▷ C2×C673 ▷ C673 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|a^2=c,c^2=d,b^a=bd,e^a=e^58,e^c=e^672682 conjugacy classes — view the full character table.
| maximal subgroup of | #36340537, #36340538, C2×#24924652, … |
| maximal normal subgroup of | #36340537, #36340538, C2×#24924652, … |
| maximal quotient of | #36340532, C22⋊#19129094, #36340544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 49);