Finite Group DatabasebetaFinite Group Databasebeta| order | 11892 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C991⋊C3) |
| unambiguous semidirect product | C991⋊A4 |
| Fitting, socle, derived, Hall | C22×C991 ⋊ C3 |
| Sylow | C991 ⋊ A4 |
| Sylow | C22 ⋊ C991⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C991 | C3 |
| LCS | G ▷ C22×C991 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,991|b^a=c,c^a=bc,d^a=d^1131324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C991⋊C3, C3×C22⋊(C991⋊C3) |
| maximal normal subgroup of | A4×C991⋊C3, C3×C22⋊(C991⋊C3) |
| maximal quotient of | C22⋊#22581943, C3×C22⋊(C991⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11892, 10);