Finite Group DatabasebetaFinite Group Databasebeta| order | 11972 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#64408 |
| Fitting, socle, Hall | C41×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #64408 |
| commutator, hypocenter | C73 | C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C41×C73 | C4 |
| prime radical | C41×D73 | C2 |
| cosocle | D73 | C2×C41 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C41 | |
12 conjugacy classes of subgroups.
902 conjugacy classes — view the full character table.
| maximal subgroup of | C41×#64408⋊C3, C3×C41×#64408, C41×C3⋊#64408 |
| maximal normal subgroup of | C41×#64408⋊C3, C3×C41×#64408 |
| maximal quotient of | C3×C41×#64408, C41×C3⋊#64408 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11972, 6);