Finite Group DatabasebetaFinite Group Databasebeta| order | 11004 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic917 |
| unambiguous semidirect product | C131⋊(C3×Dic7) |
| derived, Hall | C7×C131 ⋊ C3×C4 |
| Hall | C3×C7×C131 ⋊ C4 |
| Hall | C3×C131 ⋊ Dic7 |
| Sylow | C131 ⋊ C3×Dic7 |
| Hall | C3×C7 ⋊ Dic131 |
| Sylow | C7 ⋊ C3×Dic131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D917 |
| commutator, hypocenter | C7×C131 | C3×C4 |
| Frattini | C2 | C3×D917 |
| Fitting, socle, prime radical | C2×C3×C7×C131 | C2 |
| cosocle | C2×C7×C131 | C2×C3 |
| LCS | G ▷ C7×C131 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
2760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic917, (C7⋊C9)⋊Dic131, C3×ΓL(1,𝔽8)⋊Dic131, … |
| maximal normal subgroup of | C9×Dic917, (C7⋊C9)⋊Dic131, C3×ΓL(1,𝔽8)⋊Dic131, … |
| maximal quotient of | C9×Dic917, C3×Dic2751, C32×Dic917 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11004, 5);