Finite Group DatabasebetaFinite Group Databasebeta| order | 12027 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C211 ⋊ C3 |
| Sylow | C211 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C211⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C211 | C3 |
| LCS | G ▷ C19×C211 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,19,211|b^a=b^7,c^a=c^141339 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#26046683, #37562589, #37562593, … |
| maximal normal subgroup of | C2×#26046683, #37562589, #37562593, … |
| maximal quotient of | C2×#26046683, #49115289, C3×#26046683 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12027, 3);