Finite Group DatabasebetaFinite Group Databasebeta| order | 10768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C673 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14582089 |
| commutator, hypocenter | C673 | C2×C8 |
| Frattini | C2 | C2×#14582089 |
| Fitting | C4×C673 | C4 |
| socle | C2×C673 | C2×C4 |
| prime radical | C2×D673 | C4 |
| cosocle | Dic673 | C22 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,673|a^2=c,c^2=d,e^a=e^58,e^b=e^672,e^c=e^672688 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14582089, #36340531, #36340539, … |
| maximal normal subgroup of | C8×#14582089, #36340531, #36340539, … |
| maximal quotient of | C4×#19129094, #36340534, #36340544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10768, 48);