Finite Group DatabasebetaFinite Group Databasebeta| order | 22155 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×(C211⋊C3)⋊C5 |
| unambiguous semidirect product | (C7×C211⋊C3)⋊C5 |
| Fitting, socle, Hall | C7×C211 ⋊ C3×C5 |
| derived, Sylow | C211 ⋊ C3×C5×C7 |
| Hall | C7×C211⋊C5 ⋊ C3 |
| Hall | C7×C211⋊C3 ⋊ C5 |
| Hall | C211⋊C5 ⋊ C3×C7 |
| Hall | C211⋊C3 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C211⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C211 | C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C211 | C3×C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
203 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C7×(C211⋊C3)⋊C5, C7×(D211⋊C3)⋊C5, D7×(C211⋊C3)⋊C5, … |
| maximal normal subgroup of | C2×C7×(C211⋊C3)⋊C5, C7×(D211⋊C3)⋊C5, D7×(C211⋊C3)⋊C5, … |
| maximal quotient of | C2×C7×(C211⋊C3)⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22155, 10);