Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×C19⋊#5997 |
| Fitting, socle, Hall | C3×C72×C19 ⋊ C4 |
| derived, Hall | C72×C19 ⋊ C3×C4 |
| Hall | C3×C72 ⋊ Dic19 |
| Hall | C3×C19 ⋊ #5997 |
| Sylow | C72 ⋊ C3×Dic19 |
| Sylow | C19 ⋊ C3×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊#5997 |
| commutator, hypocenter | C72×C19 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C4 |
| prime radical | C3×C19×C7⋊D7 | C2 |
| cosocle | C19×C7⋊D7 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
750 conjugacy classes — view the full character table.
| maximal subgroup of | #45691599, #45691600, #45691603, … |
| maximal normal subgroup of | #45691599, #45691600, #45691603, … |
| maximal quotient of | C9×C19⋊#5997, C32×C19⋊#5997, C3×C3⋊(C19⋊#5997) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 270);