Finite Group DatabasebetaFinite Group Databasebeta| order | 10988 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×#4223 |
| Fitting, socle, Hall | C41×C67 ⋊ C4 |
| derived, Sylow | C41 ⋊ C4×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | #4223 |
| commutator, hypocenter | C41 | C4×C67 |
| Frattini | C1 | G |
| Fitting, socle | C41×C67 | C4 |
| prime radical | C67×D41 | C2 |
| cosocle | D41 | C2×C67 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C67 | |
12 conjugacy classes of subgroups.
938 conjugacy classes — view the full character table.
| maximal subgroup of | #4223×C67⋊C3, C3×C67×#4223, C67×C3⋊#4223 |
| maximal normal subgroup of | #4223×C67⋊C3, C3×C67×#4223 |
| maximal quotient of | C3×C67×#4223, C67×C3⋊#4223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10988, 6);