Finite Group DatabasebetaFinite Group Databasebeta| order | 12387 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C4129⋊C3 |
| Fitting, socle, derived, Sylow | C4129 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C4129 | C3 |
| LCS | G ▷ C4129 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
3,4129|b^a=b^21491379 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4129⋊C3, C2×C4129⋊C3, C3×C4129⋊C3 |
| maximal normal subgroup of | D4129⋊C3, C2×C4129⋊C3, C3×C4129⋊C3 |
| maximal quotient of | C2×C4129⋊C3, C4129⋊C9, C3×C4129⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12387, 1);