Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D917 |
| unambiguous semidirect product | (D3×C7)⋊D131 |
| unambiguous semidirect product | (D3×C131)⋊D7 |
| Fitting, socle, derived, Hall | C3×C7×C131 ⋊ C22 |
| Hall | C7×C131 ⋊ C2×D3 |
| Hall | C3×C131 ⋊ C2×D7 |
| Sylow | C131 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ C2×D131 |
| Sylow | C7 ⋊ D3×D131 |
| Sylow | C3 ⋊ C2×D917 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C131 | C22 |
| LCS | G ▷ C3×C7×C131 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1380 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D917, D3×ΓL(1,𝔽8)⋊D131, C3×D3×D917, … |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)⋊D131, C3×D3×D917 |
| maximal quotient of | D9×D917, C3×D3×D917, D3×D2751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 23);