Finite Group DatabasebetaFinite Group Databasebeta| order | 11181 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3727⋊C3 |
| Fitting, socle, derived, Sylow | C3727 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3727 | C3 |
| LCS | G ▷ C3727 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
3,3727|b^a=b^25381245 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3727⋊C3, C2×C3727⋊C3, #46776626, … |
| maximal normal subgroup of | D3727⋊C3, C2×C3727⋊C3, #46776626, … |
| maximal quotient of | C2×C3727⋊C3, #46776624, C3×C3727⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11181, 1);