Finite Group DatabasebetaFinite Group Databasebeta| order | 11972 |
| isoclinism | isoclinic class of D73 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×Dic73 |
| derived, Sylow | C73 ⋊ C4×C41 |
| Hall | C41×C73 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D73 |
| commutator, hypocenter | C73 | C4×C41 |
| Frattini | C2 | C41×D73 |
| Fitting, socle, prime radical | C2×C41×C73 | C2 |
| cosocle | C2×C73 | C2×C41 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C41 | |
12 conjugacy classes of subgroups.
3116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C41×Dic73, C41×Dic219, C41×Dic73⋊C3 |
| maximal normal subgroup of | C3×C41×Dic73, C41×Dic73⋊C3 |
| maximal quotient of | C3×C41×Dic73, C41×Dic219 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11972, 3);