Finite Group DatabasebetaFinite Group Databasebeta| order | 11892 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C991⋊C3)⋊C4 |
| unambiguous semidirect product | Dic991⋊C3 |
| derived, Sylow | C991 ⋊ C3×C4 |
| Hall | Dic991 ⋊ C3 |
| Hall | C991⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D991⋊C3 |
| commutator, hypocenter | C991 | C3×C4 |
| Fitting, socle, cosocle | C2×C991 | C2×C3 |
| prime radical | C2×C991⋊C3 | C2 |
| LCS | G ▷ C991 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,991,2|a^2=d,c^a=c^990,c^b=c^113342 conjugacy classes — view the full character table.
| maximal subgroup of | #22581945⋊C4, C3×(C991⋊C3)⋊C4, C3⋊((C991⋊C3)⋊C4) |
| maximal normal subgroup of | #22581945⋊C4, C3×(C991⋊C3)⋊C4 |
| maximal quotient of | #22581943⋊C4, C3×(C991⋊C3)⋊C4, C3⋊((C991⋊C3)⋊C4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11892, 2);