Finite Group DatabasebetaFinite Group Databasebeta| order | 1332 |
| isoclinism | isoclinic class of (C3⋊D3)⋊D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D37 |
| unambiguous semidirect product | D111⋊D3 |
| Fitting, socle, derived, Hall | C32×C37 ⋊ C22 |
| Sylow | C37 ⋊ D32 |
| Sylow | C32 ⋊ C2×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C37 | C22 |
| LCS | G ▷ C32×C37 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 222 |
Polycyclic presentation:
2^2,3^2,37|c^a=c^2,e^a=e^36,c^b=c^2,d^b=d^2117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1332, 52);