Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C131 · Schur multiplier (H2) = C2 |
| direct product | C2×D21×C131 |
| unambiguous semidirect product | (C2×C3)⋊(D7×C131) |
| unambiguous semidirect product | (C2×C7)⋊(D3×C131) |
| Fitting, socle | C2×C3×C7×C131 ⋊ C2 |
| derived, Hall | C3×C7 ⋊ C22×C131 |
| Hall | C3×C7×C131 ⋊ C22 |
| Hall | C7×C131 ⋊ C2×D3 |
| Hall | C3×C131 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D3×C131 |
| Sylow | C3 ⋊ C2×D7×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C131 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C22×C131 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C131 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C131 | |
40 conjugacy classes of subgroups.
3144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D63×C131, C2×C3⋊AGL(1,𝔽7)×C131, D3×D21×C131, … |
| maximal normal subgroup of | C2×C3⋊AGL(1,𝔽7)×C131, C2×C3×D21×C131 |
| maximal quotient of | C2×D63×C131, D3×D21×C131, C2×C3×D21×C131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 29);