Finite Group DatabasebetaFinite Group Databasebeta| order | 10456 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1307⋊C8 |
| derived, Sylow | C1307 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D1307 |
| commutator, hypocenter | C1307 | C8 |
| Fitting, cosocle | C4×C1307 | C2 |
| socle, prime radical | C2×C1307 | C4 |
| LCS | G ▷ C1307 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1307|a^2=b,b^2=c,d^a=d^13062620 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D1307, C2×C1307⋊C8, #35230010, … |
| maximal normal subgroup of | C8×D1307, C2×C1307⋊C8, #35230010, … |
| maximal quotient of | C1307⋊C16, C2×C1307⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10456, 6);