Finite Group DatabasebetaFinite Group Databasebeta| order | 6948 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic193⋊C3) |
| unambiguous semidirect product | Dic579⋊C3 |
| derived | C3×C193 ⋊ C3×C4 |
| Hall | C3×C193⋊C3 ⋊ C4 |
| Sylow | C193 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D193⋊C3) |
| commutator, hypocenter | C3×C193 | C3×C4 |
| Fitting, socle | C2×C3×C193 | C2×C3 |
| LCS | G ▷ C3×C193 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,193,2|a^2=e,c^a=c^2,d^a=d^192,d^b=d^84210 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C3⋊(Dic193⋊C3), C3⋊(Dic965⋊C3), C3⋊(#16838803⋊C3) |
| maximal normal subgroup of | C5×C3⋊(Dic193⋊C3) |
| maximal quotient of | C5×C3⋊(Dic193⋊C3), C3⋊(Dic965⋊C3), C3⋊(#16838803⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6948, 21);