Finite Group DatabasebetaFinite Group Databasebeta| order | 6222 |
| isoclinism | isoclinic class of D61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D61⋊C3 |
| unambiguous semidirect product | D61⋊(C3×C17) |
| unambiguous semidirect product | (C61⋊C3)⋊(C2×C17) |
| unambiguous semidirect product | (C17×D61)⋊C3 |
| Fitting, socle, Hall | C17×C61 ⋊ C2×C3 |
| derived, Sylow | C61 ⋊ C2×C3×C17 |
| Hall | C17×C61⋊C3 ⋊ C2 |
| Hall | C17×D61 ⋊ C3 |
| Hall | C61⋊C3 ⋊ C2×C17 |
| Hall | D61 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D61⋊C3 |
| commutator, hypocenter | C61 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C61 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#6923⋊C3, #16861898⋊C3, D17×D61⋊C3, … |
| maximal normal subgroup of | C17×#6923⋊C3, #16861898⋊C3, D17×D61⋊C3, … |
| maximal quotient of | C17×Dic61⋊C3, C2×C17×D61⋊C3, C17×D61⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6222, 10);