Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | D3×C7×D131 |
| unambiguous semidirect product | (D3×C131)⋊(C2×C7) |
| unambiguous semidirect product | (C3×D131)⋊(C2×C7) |
| unambiguous semidirect product | D393⋊(C2×C7) |
| Fitting, socle, Hall | C3×C7×C131 ⋊ C22 |
| derived, Hall | C3×C131 ⋊ C22×C7 |
| Hall | C7×C131 ⋊ C2×D3 |
| Sylow | C131 ⋊ C2×D3×C7 |
| Hall | C3×C7 ⋊ C2×D131 |
| Sylow | C3 ⋊ C2×C7×D131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×D131 |
| commutator, cosocle, hypocenter | C3×C131 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C131 | C22 |
| LCS | G ▷ C3×C131 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
1407 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D9×D131, D3×ΓL(1,𝔽8)×D131, C3×D3×C7×D131, … |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)×D131, C3×D3×C7×D131 |
| maximal quotient of | C7×D9×D131, C3×D3×C7×D131, D3×C7×D393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 19);