Finite Group DatabasebetaFinite Group Databasebeta| order | 8732 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×Dic37 |
| derived, Sylow | C37 ⋊ C4×C59 |
| Hall | C37×C59 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C59 | D37 |
| commutator, hypocenter | C37 | C4×C59 |
| Frattini | C2 | C59×D37 |
| Fitting, socle | C2×C37×C59 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C59 | |
12 conjugacy classes of subgroups.
2360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C59×Dic37, C59×Dic111, C59×Dic37⋊C3 |
| maximal normal subgroup of | C3×C59×Dic37, C59×Dic37⋊C3 |
| maximal quotient of | C3×C59×Dic37, C59×Dic111 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8732, 2);