Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D7×D57 |
| unambiguous semidirect product | (C3×D7)⋊(C7×D19) |
| unambiguous semidirect product | (D7×C19)⋊(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 ⋊ C2×D57 |
| Sylow | C19 ⋊ D3×C7×D7 |
| Sylow | C3 ⋊ C7×D7×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×D57 |
| 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.
1050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×D171, D57×#64418, C7×#11716325⋊D3, … |
| maximal normal subgroup of | C7×#11716325⋊D3, C7×#11716326⋊D3, C7×AGL(1,𝔽7)×D57, … |
| maximal quotient of | C7×D7×D171, C3×C7×D7×D57, C7×D21×D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 274);