Finite Group DatabasebetaFinite Group Databasebeta| order | 11998 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D857 |
| unambiguous semidirect product | C857⋊(C2×C7) |
| Fitting, socle, Hall | C7×C857 ⋊ C2 |
| derived, Sylow | C857 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D857 |
| commutator, cosocle, hypocenter | C857 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C857 | C2 |
| LCS | G ▷ C857 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
3010 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#16812170, C7⋊#16812170, D7×D857, … |
| maximal normal subgroup of | C7×#16812170, C7⋊#16812170, D7×D857, … |
| maximal quotient of | C7×Dic857, C2×C7×D857, C3×C7×D857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11998, 2);