Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×Dic69 |
| unambiguous semidirect product | C3⋊(C37×Dic23) |
| unambiguous semidirect product | C23⋊(Dic3×C37) |
| derived, Hall | C3×C23 ⋊ C4×C37 |
| Hall | C3×C23×C37 ⋊ C4 |
| Hall | C23×C37 ⋊ Dic3 |
| Hall | C3×C37 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic3×C37 |
| Sylow | C3 ⋊ C37×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D69 |
| commutator, hypocenter | C3×C23 | C4×C37 |
| Frattini | C2 | C37×D69 |
| Fitting, socle, prime radical | C2×C3×C23×C37 | C2 |
| cosocle | C2×C3×C23 | C2×C37 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C37 | |
24 conjugacy classes of subgroups.
2664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×Dic207, C37⋊C3×Dic69, C37×C3⋊Dic69, … |
| maximal normal subgroup of | C37⋊C3×Dic69, C3×C37×Dic69 |
| maximal quotient of | C37×Dic207, C37×C3⋊Dic69, C3×C37×Dic69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 8);