Finite Group DatabasebetaFinite Group Databasebeta| order | 8418 |
| isoclinism | isoclinic class of D61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D61⋊C3 |
| unambiguous semidirect product | D61⋊(C3×C23) |
| unambiguous semidirect product | (C61⋊C3)⋊(C2×C23) |
| unambiguous semidirect product | (C23×D61)⋊C3 |
| Fitting, socle, Hall | C23×C61 ⋊ C2×C3 |
| derived, Sylow | C61 ⋊ C2×C3×C23 |
| Hall | C23×C61⋊C3 ⋊ C2 |
| Hall | C23×D61 ⋊ C3 |
| Hall | C61⋊C3 ⋊ C2×C23 |
| Hall | D61 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D61⋊C3 |
| commutator, hypocenter | C61 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C61 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
368 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#6923⋊C3, C23⋊(#6923⋊C3), D23×D61⋊C3, … |
| maximal normal subgroup of | C23×#6923⋊C3, C23⋊(#6923⋊C3), D23×D61⋊C3, … |
| maximal quotient of | C23×Dic61⋊C3, C2×C23×D61⋊C3, C23×D61⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8418, 10);