Finite Group DatabasebetaFinite Group Databasebeta| order | 6948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D579 |
| unambiguous semidirect product | (C3×D3)⋊D193 |
| unambiguous semidirect product | (D3×C193)⋊D3 |
| Fitting, socle, derived, Hall | C32×C193 ⋊ C22 |
| Sylow | C193 ⋊ D32 |
| Sylow | C32 ⋊ C2×D193 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C193 | C22 |
| LCS | G ▷ C32×C193 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
873 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×D579, D3×D2895, D15×D579, … |
| maximal normal subgroup of | C5×D3×D579 |
| maximal quotient of | C5×D3×D579, D3×D2895, D15×D579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6948, 43);