Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×C32×C3⋊#157 |
| unambiguous semidirect product | (C2×C3)⋊(C32×#157) |
| Fitting, socle | C2×C35 ⋊ C4 |
| derived | C33 ⋊ C2×C32×C4 |
| Sylow | C35 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C3⋊#157 |
| commutator, hypocenter | C33 | C2×C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C35 | C4 |
| prime radical | C2×C33×C3⋊D3 | C2 |
| cosocle | C3×C3⋊D3 | C22×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C32 | |
1800 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 1800 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3952);