Finite Group DatabasebetaFinite Group Databasebeta| order | 6948 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#11715871 |
| Fitting, Hall | C9×C193 ⋊ C4 |
| derived, Sylow | C193 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #11715871 |
| commutator, hypocenter | C193 | C4×C9 |
| Frattini | C3 | C3×#11715871 |
| Fitting | C9×C193 | C4 |
| socle | C3×C193 | C3×C4 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C9 | |
18 conjugacy classes of subgroups.
468 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9×#11715871, C9×#16838801, C9×#16838802, … |
| maximal normal subgroup of | C5×C9×#11715871 |
| maximal quotient of | C5×C9×#11715871, C9×#16838801, C9×#16838802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6948, 10);