Finite Group DatabasebetaFinite Group Databasebeta| order | 16502 |
| isoclinism | isoclinic class of D223 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D223 |
| Fitting, socle, Hall | C37×C223 ⋊ C2 |
| derived, Sylow | C223 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D223 |
| commutator, cosocle, hypocenter | C223 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C223 | C2 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C37 | |
8 conjugacy classes of subgroups.
4181 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×D223, C2×C37×D223, C3×C37×D223, … |
| maximal normal subgroup of | D37×D223, C2×C37×D223, C3×C37×D223, … |
| maximal quotient of | C37×Dic223, C2×C37×D223, C3×C37×D223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16502, 4);