Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#10596868 |
| derived, Hall | #3862 ⋊ C4×C19 |
| Hall | C19×#3862 ⋊ C4 |
| Hall | C72×C19 ⋊ Dic3 |
| Sylow | C72 ⋊ Dic3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | #64418 |
| commutator, hypocenter | #3862 | C4×C19 |
| Frattini | C2 | C19×#64418 |
| Fitting, socle | C2×C72×C19 | D3 |
| prime radical | C2×C19×#3862 | C2 |
| cosocle | C2×#3862 | C2×C19 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C2×C19 | |
44 conjugacy classes of subgroups.
760 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10596868⋊C3, #45691811, #45691812, … |
| maximal normal subgroup of | C19×#10596868⋊C3, #45691811, #45691812, … |
| maximal quotient of | C19×#13183527, C3×C19×#10596868, C19×C3⋊#10596868 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 119);