Finite Group DatabasebetaFinite Group Databasebeta| order | 10072 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1259⋊C8 |
| derived, Sylow | C1259 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D1259 |
| commutator, hypocenter | C1259 | C8 |
| Fitting, cosocle | C4×C1259 | C2 |
| socle, prime radical | C2×C1259 | C4 |
| LCS | G ▷ C1259 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1259|a^2=b,b^2=c,d^a=d^12582524 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D1259, C2×C1259⋊C8, #34117851, … |
| maximal normal subgroup of | C8×D1259, C2×C1259⋊C8, #34117851, … |
| maximal quotient of | C1259⋊C16, C2×C1259⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10072, 6);