Finite Group DatabasebetaFinite Group Databasebeta| order | 22155 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C211⋊C3)⋊C5)⋊C7 |
| unambiguous semidirect product | ((C211⋊C3)⋊C7)⋊C5 |
| unambiguous semidirect product | ((C211⋊C5)⋊C7)⋊C3 |
| Fitting, socle, derived, Sylow | C211 ⋊ C3×C5×C7 |
| Hall | (C211⋊C5)⋊C7 ⋊ C3 |
| Hall | (C211⋊C3)⋊C7 ⋊ C5 |
| Hall | (C211⋊C3)⋊C5 ⋊ C7 |
| Hall | C211⋊C7 ⋊ C3×C5 |
| Hall | C211⋊C5 ⋊ C3×C7 |
| Hall | C211⋊C3 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C211 | C3×C5×C7 |
| LCS | G ▷ C211 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,7,211|d^a=d^196,d^b=d^107,d^c=d^171107 conjugacy classes — view the full character table.
| maximal subgroup of | C2×((C211⋊C3)⋊C5)⋊C7, AGL(1,𝔽211) |
| maximal normal subgroup of | C2×((C211⋊C3)⋊C5)⋊C7, AGL(1,𝔽211) |
| maximal quotient of | C2×((C211⋊C3)⋊C5)⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22155, 14);