Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D19×D21 |
| unambiguous semidirect product | (C3×D19)⋊(C7×D7) |
| unambiguous semidirect product | (C7×D19)⋊(D3×C7) |
| Fitting, socle, Hall | C3×C72×C19 ⋊ C22 |
| derived | C3×C7×C19 ⋊ C22×C7 |
| Hall | C72×C19 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ D3×D19 |
| Sylow | C19 ⋊ C2×C7×D21 |
| Sylow | C3 ⋊ C7×D7×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D19×D21 |
| commutator, cosocle, hypocenter | C3×C7×C19 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C22 |
| LCS | G ▷ C3×C7×C19 | |
| UCS | C1 ◁ C7 | |
104 conjugacy classes of subgroups.
924 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 272);