Finite Group DatabasebetaFinite Group Databasebeta| order | 11892 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic991 |
| derived, Sylow | C991 ⋊ C3×C4 |
| Hall | C3×C991 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D991 |
| commutator, hypocenter | C991 | C3×C4 |
| Frattini | C2 | C3×D991 |
| Fitting, socle, prime radical | C2×C3×C991 | C2 |
| cosocle | C2×C991 | C2×C3 |
| LCS | G ▷ C991 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
2982 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #22581943⋊C4, C9×Dic991, C3×(C991⋊C3)⋊C4, … |
| maximal normal subgroup of | #22581943⋊C4, C9×Dic991, C3×(C991⋊C3)⋊C4, … |
| maximal quotient of | C9×Dic991, C3×Dic2973, C32×Dic991 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11892, 5);