Finite Group DatabasebetaFinite Group Databasebeta| order | 6954 |
| isoclinism | isoclinic class of C61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C2×C19×C61⋊C3 |
| unambiguous semidirect product | (C2×C61)⋊(C3×C19) |
| Fitting, socle, Hall | C2×C19×C61 ⋊ C3 |
| derived, Sylow | C61 ⋊ C2×C3×C19 |
| Hall | C19×C61 ⋊ C2×C3 |
| Hall | C2×C61 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | C61⋊C3 |
| commutator, hypocenter | C61 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C61 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C19 | |
16 conjugacy classes of subgroups.
874 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C19×C61⋊C3, C19×Dic61⋊C3, Dic19×C61⋊C3, … |
| maximal normal subgroup of | C4×C19×C61⋊C3, C19×Dic61⋊C3, Dic19×C61⋊C3, … |
| maximal quotient of | C4×C19×C61⋊C3, C22×C19×C61⋊C3, C2×C19×C61⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6954, 2);