Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D393 |
| unambiguous semidirect product | (C3×D7)⋊D131 |
| unambiguous semidirect product | (D7×C131)⋊D3 |
| 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 ⋊ C2×D393 |
| Sylow | C3 ⋊ D7×D131 |
| 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.
990 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D1179, AGL(1,𝔽7)×D393, C3×D7×D393, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D393, C3×D7×D393 |
| maximal quotient of | D7×D1179, C3×D7×D393, D21×D393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 22);