Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D7×D131 |
| Fitting, socle, Hall | C3×C7×C131 ⋊ C22 |
| derived, Hall | C7×C131 ⋊ C22×C3 |
| Hall | C3×C131 ⋊ C2×D7 |
| Sylow | C131 ⋊ C2×C3×D7 |
| Hall | C3×C7 ⋊ C2×D131 |
| Sylow | C7 ⋊ C2×C3×D131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×D131 |
| commutator, cosocle, hypocenter | C7×C131 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C131 | C22 |
| LCS | G ▷ C7×C131 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
1005 conjugacy classes — view the full character table.
| maximal subgroup of | D7⋊C9×D131, C9×D7×D131, C3×AGL(1,𝔽7)×D131, … |
| maximal normal subgroup of | D7⋊C9×D131, C9×D7×D131, C3×AGL(1,𝔽7)×D131, … |
| maximal quotient of | C9×D7×D131, C32×D7×D131, C3×D21×D131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 18);