Finite Group DatabasebetaFinite Group Databasebeta| order | 11198 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D509 |
| unambiguous semidirect product | C509⋊(C2×C11) |
| Fitting, socle, Hall | C11×C509 ⋊ C2 |
| derived, Sylow | C509 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D509 |
| commutator, cosocle, hypocenter | C509 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C509 | C2 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
2816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#14523266, C11⋊#14523266, D11×D509, … |
| maximal normal subgroup of | C11×#14523266, C11⋊#14523266, D11×D509, … |
| maximal quotient of | C11×Dic509, C2×C11×D509, C3×C11×D509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11198, 2);