Finite Group DatabasebetaFinite Group Databasebeta| order | 22155 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C211⋊C7 |
| unambiguous semidirect product | (C3×C5×C211)⋊C7 |
| Fitting, socle, Hall | C3×C5×C211 ⋊ C7 |
| derived, Sylow | C211 ⋊ C3×C5×C7 |
| Hall | C5×C211 ⋊ C3×C7 |
| Hall | C3×C211 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C211⋊C7 |
| commutator, cosocle, hypocenter | C211 | C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C211 | C7 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
555 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C5×C211⋊C7, C3×C5×D211⋊C7, C3×D5×C211⋊C7, … |
| maximal normal subgroup of | C2×C3×C5×C211⋊C7, C3×C5×D211⋊C7, C3×D5×C211⋊C7, … |
| maximal quotient of | C2×C3×C5×C211⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22155, 2);