Finite Group DatabasebetaFinite Group Databasebeta| order | 3736 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C467⋊C8 |
| derived, Sylow | C467 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D467 |
| commutator, hypocenter | C467 | C8 |
| Fitting, cosocle | C4×C467 | C2 |
| socle, prime radical | C2×C467 | C4 |
| LCS | G ▷ C467 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 475 |
| transitive degree | μt(G) = 3736 |
Polycyclic presentation:
2^3,467|a^2=b,b^2=c,d^a=d^466940 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3736, 6);