Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C131 · Schur multiplier (H2) = C1 |
| direct product | Dic21×C131 |
| unambiguous semidirect product | C3⋊(Dic7×C131) |
| unambiguous semidirect product | C7⋊(Dic3×C131) |
| derived, Hall | C3×C7 ⋊ C4×C131 |
| Hall | C3×C7×C131 ⋊ C4 |
| Hall | C7×C131 ⋊ Dic3 |
| Hall | C3×C131 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic3×C131 |
| Sylow | C3 ⋊ Dic7×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C131 | D21 |
| commutator, hypocenter | C3×C7 | C4×C131 |
| Frattini | C2 | D21×C131 |
| Fitting, socle, prime radical | C2×C3×C7×C131 | C2 |
| cosocle | C2×C3×C7 | C2×C131 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C131 | |
24 conjugacy classes of subgroups.
3144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×Dic63, C131×C3⋊(ΓL(1,𝔽8)⋊C4), C131×C3⋊Dic21, … |
| maximal normal subgroup of | C131×C3⋊(ΓL(1,𝔽8)⋊C4), C3×Dic21×C131 |
| maximal quotient of | C131×Dic63, C131×C3⋊Dic21, C3×Dic21×C131 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 8);