Finite Group DatabasebetaFinite Group Databasebeta| order | 6948 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C4×C193⋊C3 |
| unambiguous semidirect product | (C4×C193)⋊C32 |
| unambiguous semidirect product | (C3×C4×C193)⋊C3 |
| Fitting | C3×C4×C193 ⋊ C3 |
| derived, Sylow | C193 ⋊ C32×C4 |
| Hall | C4×C193 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C193⋊C3 |
| commutator, hypocenter | C193 | C32×C4 |
| Frattini | C2 | C2×C3×C193⋊C3 |
| Fitting | C3×C4×C193 | C3 |
| socle | C2×C3×C193 | C2×C3 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C3×C4 | |
36 conjugacy classes of subgroups.
804 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic5×C193⋊C3, C3×C4×C5×C193⋊C3, C3×AGL(1,𝔽5)×C193⋊C3 |
| maximal normal subgroup of | C3×C4×C5×C193⋊C3 |
| maximal quotient of | C3×Dic5×C193⋊C3, C3×C4×C5×C193⋊C3, C3×AGL(1,𝔽5)×C193⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6948, 23);