Finite Group DatabasebetaFinite Group Databasebeta| order | 1332 |
| isoclinism | isoclinic class of #66526⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C37 ⋊ C4×C9 |
| Hall | #66526 ⋊ C4 |
| Hall | Dic37 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #66526⋊C2 |
| commutator, hypocenter | C37 | C4×C9 |
| Fitting, socle | C2×C37 | C2×C9 |
| prime radical, cosocle | C2×C37⋊C3 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 148 |
Polycyclic presentation:
2,3,2,3,37|a^2=c,b^3=d,e^a=e^36,e^b=e^34,e^d=e^1040 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1332, 19);