Finite Group DatabasebetaFinite Group Databasebeta| order | 6948 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic193⋊C9 |
| derived, Sylow | C193 ⋊ C4×C9 |
| Hall | C193⋊C9 ⋊ C4 |
| Hall | Dic193 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D193⋊C3 |
| commutator, hypocenter | C193 | C4×C9 |
| Fitting, socle | C2×C3×C193 | C2×C3 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C2×C3 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,193,2,3|a^2=d,b^3=e,c^a=c^192,c^b=c^84228 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic193⋊C9, Dic965⋊C9, #16838803⋊C9 |
| maximal normal subgroup of | C5×Dic193⋊C9 |
| maximal quotient of | C5×Dic193⋊C9, Dic965⋊C9, #16838803⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6948, 2);