Finite Group DatabasebetaFinite Group Databasebeta| order | 11172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D21×D133 |
| Fitting, socle, derived, Hall | C3×C72×C19 ⋊ C22 |
| Hall | C72×C19 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ D72 |
| Sylow | C72 ⋊ D3×D19 |
| Sylow | C19 ⋊ D7×D21 |
| Sylow | C3 ⋊ D7×D133 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C22 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
816 conjugacy classes — view the full character table.
| maximal subgroup of | D63×D133, #45692279, #45692321, … |
| maximal normal subgroup of | #45692321, #45692322, C3⋊AGL(1,𝔽7)×D133, … |
| maximal quotient of | D63×D133, C3×D21×D133, D21×D399, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11172, 284);