Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D21×D131 |
| unambiguous semidirect product | (C3×D131)⋊D7 |
| unambiguous semidirect product | (C7×D131)⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C131 ⋊ C22 |
| Hall | C7×C131 ⋊ C2×D3 |
| Hall | C3×C131 ⋊ C2×D7 |
| Sylow | C131 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×D131 |
| Sylow | C7 ⋊ D3×D131 |
| 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.
804 conjugacy classes — view the full character table.
| maximal subgroup of | D63×D131, C3⋊AGL(1,𝔽7)×D131, C3×D21×D131, … |
| maximal normal subgroup of | C3⋊AGL(1,𝔽7)×D131, C3×D21×D131 |
| maximal quotient of | D63×D131, C3×D21×D131, D393⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 20);