Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×D21⋊D7 |
| unambiguous semidirect product | D21⋊(D7×C19) |
| Fitting, socle, Hall | C3×C72×C19 ⋊ C22 |
| derived, Hall | C3×C72 ⋊ C22×C19 |
| Hall | C72×C19 ⋊ C2×D3 |
| Hall | C3×C19 ⋊ D72 |
| Sylow | C72 ⋊ C2×D3×C19 |
| Sylow | C3 ⋊ D72×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D21⋊D7 |
| commutator, cosocle, hypocenter | C3×C72 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C22 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C19 | |
104 conjugacy classes of subgroups.
969 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#11725071⋊C2, C19×D63⋊D7, C19×#13183625, … |
| maximal normal subgroup of | C19×(C3⋊AGL(1,𝔽7))⋊D7, #45692349, #45692350, … |
| maximal quotient of | C19×D63⋊D7, C3×C19×D21⋊D7, C19×D21⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 286);