Finite Group DatabasebetaFinite Group Databasebeta| order | 36668 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×Dic103 |
| unambiguous semidirect product | C103⋊(C4×C89) |
| derived, Sylow | C103 ⋊ C4×C89 |
| Hall | C89×C103 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C89 | D103 |
| commutator, hypocenter | C103 | C4×C89 |
| Frattini | C2 | C89×D103 |
| Fitting, socle, prime radical | C2×C89×C103 | C2 |
| cosocle | C2×C103 | C2×C89 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C2×C89 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36668 |
9434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36668, 3);